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Chapter: 8 -Problem: 13 >> Find the volume of the solid of revolution formed by rotating about the x-axis each region bounded by the given curves.ƒ(x) = ?2x + 1, y = 0, x = 1, x = 4
Answer Preview: x 2x 1 y 0 x 1 x …

, Chapter: 2 -Problem: 33 >> Graph each of the following.y = 5ex + 2
Answer Preview: Graph of y 5…

, Chapter: 12 -Problem: 17 >> Find Taylor polynomials of degree 4 at 0 for the functions defined as follows.ƒ(x) = e2-x
Answer Preview: Derivative f x e x e e x x e …

, Chapter: 8 -Problem: 55 >> The United States has been steadily reducing its production of veal in recent decades. Annual U.S. veal production (in millions of pounds) can be approximated by p(t) = 663e-0.042t, where t is the number of years since 1970. Assuming this trend continues, estimate the total amount of veal produced in the U.S. from the year 2000 on.
Answer Preview: Annual production can be estimated to be 4478 million …

, Chapter: 9 -Problem: 53 >> Extra postage is charged for parcels sent by U.S. mail that are more than 84 in. in length and girth combined. (Girth is the distance around the parcel perpendicular to its length. See the figure.) Express the combined length and girth as a function of L, W, and H. Transcribed Image Text: H L W Leng
Answer Preview: The gir…

, Chapter: 6 -Problem: 55 >> Researchers have found a correlation between respiratory rate and body mass in the first three years of life. This correlation can be expressed by the function log R(w) = 1.83 - 0.43 log(w), where w is the body weight (in kilograms) and R(w) is the respiratory rate (in breaths per minute).(a) Find R?(w) using implicit differentiation. (b) Find R?(w) by first solving the equation for R(w).
Answer Preview: First note that a b if t…

, Chapter: 7 -Problem: 31 >> Repeat Exercise 30 using the demand curve for a fruit juice (in dollars per liter) given byfor 0 ? q ? 25, where q is the demand in liters. Estimate the total revenue using rectangles of 5 liters' width. Transcribed Image Text: D (q) = 2 59 125 4 59 9 + 15
Answer Preview: The demand function is Left endpoints Compute valu…

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, Chapter: 2 -Problem: 20 >> List the ordered pairs obtained from each equation, given {-2, - 1, 0, 1, 2, 3} as the domain. Graph each set of ordered pairs. Give the range.y = -4x2
Answer Preview: y 4x 2 2 1 0 1 2 2 3 …

, Chapter: 5 -Problem: 49 >> (a) For the function in Exercise 19, find the average of the critical numbers.(b) For the function in Exercise 19, use a graphing calculator to find the roots of the function, and then find the average of those roots. (c) Compare your answers to parts (a) and (b). What do you notice? (d) Repeat part (a) for the function in Exercise 21. (e) Repeat part (b) for the function in Exercise 21. (f) Compa
Answer Preview: a The critical number are 3 and 4 The average is b Use a graphing calculator to fin…

, Chapter: 5 -Problem: 27 >> For each function, find (a) The critical numbers; (b) The open intervals where the function is increasing;  (c) The open intervals where it is decreasing.f(x) = x2/3
Answer Preview: Given the function f x x 2 3 let s find its critical numbers increasing intervals and decreasing int…

, Chapter: 5 -Problem: 28 >> In Exercises, find ƒ??(x), the third derivative of ƒ, and ƒ(4)(x), the fourth derivative of ƒ, for each function. Transcribed Image Text: f(x) = x + 1 X
Answer Preview: f x f x x 1 X 1 x …

, Chapter: 1 -Problem: 19 >> Describe what fixed costs and marginal costs mean to a company.
Answer Preview: The fixed cost is constant for a particular product and does …

, Chapter: 3 -Problem: 87 >> Use a graphing calculator to graph the function. (a) Determine the limit from the graph. (b) Explain how your answer could be determined from the expression for f (x). Transcribed Image Text: lim X118 ?36x² + 2x + 7 3x
Answer Preview: Graph this function on a graphing calculator A g…

, Chapter: 4 -Problem: 92 >> Over time, the number of original basic words in a language tends to decrease as words become obsolete or are replaced with new words. Linguists have used calculus to study this phenomenon and have developed a methodology for dating a language, called glottochronology. Experiments have indicated that a good estimate of the number of words that remain in use at a given time is given by N(t) = N0 e-
Answer Preview: a The number of words predicted to be in use in 1950 is 169 …

, Chapter: 5 -Problem: 75 >> A projectile is shot straight up with an initial velocity of 512 ft per second. Its height above the ground after t seconds is given by s(t) = 512t - 16t2.(a) Find the velocity and acceleration after t seconds. (b) What is the maximum height attained? (c) When does the projectile hit the ground and with what velocity?
Answer Preview: a b The maximum height is attained when The height reaches …

, Chapter: 4 -Problem: 42 >> Find all points on the graph of ƒ(x) = x3 + 9x2 + 19x - 10 where the slope of the tangent line is -5.
Answer Preview: x x 3 9x 2 19x 10 x 3x 3 18x 19x If the slope of the tangen…

, Chapter: 8 -Problem: 16 >> Find each integral, using techniques from this or the previous chapter. Transcribed Image Text: xe do
Answer Preview: fre xex dx Let …

, Chapter: 2 -Problem: 41 >> Use natural logarithms to evaluate each logarithm to the nearest thousandth.log5 30
Answer Preview: log5 30 …

, Chapter: 12 -Problem: 20 >> Use l’Hospital’s rule where applicable to find each limit. Transcribed Image Text: ?x - 3 9 lim x 9 x
Answer Preview: The limit in the numerator is 0 as is the …

, Chapter: 1 -Problem: 28 >> Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.a3 – 216
Answer Preview: The given polynomial is a 3 216 We can notice that 216 is the cube of 6 6 3 216 So we can re…

, Chapter: 8 -Problem: 2 >> The total money flow is found by taking the derivative of the function giving the rate of money flow.Determine whether each statement is true or false, and explain why.
Answer Preview: False The total money flo…

, Chapter: 9 -Problem: 49 >> In Exercises, find all points where the functions defined below have any relative extrema. Find any saddle points. Transcribed Image Text: Z || 1 -x² + 2 1 2 + 2xy = 5x - 7y + 10 -
Answer Preview: Setting z x z y 0 and solving yiel…

, Chapter: 6 -Problem: 54 >> Researchers found the demand for milk in Mexico for a particular year can be estimated by the implicit equation ln q = C - 0.678 ln p, where p represents the price of a unit of fluid milk and C represents a constant that can be calculated uniquely for a particular year. Here q represents the annual per capita fluid milk demand.(a) Use implicit differentiation to calculate and interpret the elastic
Answer Preview: a E is less than 1 so the demand is i…

, Chapter: 7 -Problem: 66 >> If ƒ(x) is the instantaneous death rate for members of a population at time x, then the number of individuals who survive to age T is given byIn 1825, the biologist Benjamin Gompertz proposed that ƒ(x) = kbx. Find a formula for F(T). Transcribed Image Text: T ·(²² f(x) dx. 0 F(T) =
Answer Preview: S 0 F T T S T So KST …

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, Chapter: 1 -Problem: 52 >> You may have heard that the average temperature of the human body is 98.6°. Recent experiments show that the actual figure is closer to 98.2°. The figure of 98.6 comes from experiments done by Carl Wunderlich in 1868. But Wunderlich measured the temperatures in degrees Celsius and rounded the average to the nearest degree, giving 37°C as the average temperature. (a) What is the Fahrenheit equivale
Answer Preview: Use the formula der…

, Chapter: 13 -Problem: 88 >> When a light ray travels from one medium, such as air, to another medium, such as water or glass, the speed of the light changes, and the direction that the ray is traveling changes. (This is why a fish under water is in a different position from the place at which it appears to be.) These changes are given by Snell’s law,where c1 is the speed in the first medium, c2 is the speed in the second med
Answer Preview: Solving 2 sin sin 0 C…

, Chapter: 4 -Problem: 22 >> Find the derivative of each function defined as follows.h(x) = (x2 – 1)3
Answer Preview: To find the derivative of the function h x x 2 1 3 with respect to x you can use the c…

, Chapter: 5 -Problem: 16 >> In Exercises, complete the following for each function.(a) Find intervals where the function is increasing or decreasing, and determine any relative extrema. (b) Find intervals where the function is concave upward or concave downward, and determine any inflection points. (c) Graph each function, considering the domain, critical points, symmetry, relative extrema, regions where the function is incr
Answer Preview: Since f x does not exist when x 0 the domain is 0 U 0 The graph is not symmetric about the y …

, Chapter: 1 -Problem: 22 >> Find the slope for each line that has a slope.3y - 1 = 14
Answer Preview: This is a horizon…

, Chapter: 2 -Problem: 76 >> Draw a sketch of the arch or culvert on coordinate axes, with the horizontal and vertical axes through the vertex of the parabola. Use the given information to label points on the parabola. Then give the equation of the parabola and answer the question.A culvert is shaped like a parabola, 18 ft across the top and 12 ft deep. How wide is the culvert 8 ft from the top?
Answer Preview: Sketch the culvert on the xy axes as a parabola that opens upward with …

, Chapter: 4 -Problem: 16 >> In Exercises, find the derivative of each function.y = 5x-5 - 6x-2 + 13x-1
Answer Preview: y 5x 5 6x 13x d…

, Chapter: 5 -Problem: 92 >> The percent of concentration of a drug in the bloodstream t hours after the drug is administered is given by(a) Find the time at which the concentration is a maximum. (b) Find the maximum concentration. Transcribed Image Text: K(t) = 4t 31² + 27
Answer Preview: a For this application the domain of K is 0 so the only critical number is 3 To determ…

, Chapter: 4 -Problem: 26 >> In Exercises, find the derivative of each function. Transcribed Image Text: g(x) = x³ - 4x Vx
Answer Preview: g x 4x 43 4 x x …

, Chapter: 8 -Problem: 8 >> Find the volume of the solid of revolution formed by rotating about the x-axis each region bounded by the given curves.ƒ(x) = x - 4, y = 0, x = 4, x = 10
Answer Preview: f x x 4 y 0 x 4 …

, Chapter: 2 -Problem: 35 >> In Exercises, find any horizontal and vertical asymptotes and any holes that may exist for each rational function. Draw the graph of each function, including any x- and y-intercepts. Transcribed Image Text: y || 2x x - 3
Answer Preview: y 3 X 3 0 when x 3 so the line x 3 is a vertical asymptote 97 194 14 10 1 94 1 …

, Chapter: 12 -Problem: 19 >> For each sequence that is geometric, find r and an.4, 16, 64, 256,...
Answer Preview: 4 16 64 256 Si…

, Chapter: 1 -Problem: 45 >> Solve each inequality.(k – 1)/(k + 2) > 1
Answer Preview: To solve the inequality k 1 k 2 1 we ll need to consider different cases based on the values of k …

, Chapter: 8 -Problem: 53 >> Assume that each function gives the rate of flow of money in dollars per year over the given period, with continuous compounding at the given annual interest rate. Find the accumulated amount of money flow at the end of the time period.ƒ(t) = 500e-0.04t, 8 years, 10%
Answer Preview: The accumulated value is 5354 97 500e …

, Chapter: 9 -Problem: 62 >> Use the total differential to approximate each quantity. Then use a calculator to approximate the quantity, and give the absolute value of the difference in the two results to 4 decimal places. Transcribed Image Text: V4.06 0.04
Answer Preview: To approximate 4 06e 0 04 let x 4 dx 0 06 y 0 and d…

, Chapter: 6 -Problem: 50 >> For the Beverton-Holt model for cod in the previous exercise, consider harvesting at a rate proportional to each year’s population, so that the population next year is given bywhere r is a positive constant of proportionality. Find the value of S that maximizes ƒ(S), and describe in words what this means. Transcribed Image
Answer Preview: Find the critical numbers S…

, Chapter: 7 -Problem: 78 >> In the 1999 movie October Sky, Homer Hickam was accused of launching a rocket that started a forest fire. Homer proved his innocence by showing that his rocket could not have flown far enough to reach where the fire started. He used the following reasoning.(a) Using the fact that a(t) = -32 (see Example 10(a)), find v(t) and s(t), given v(0) V0 and s(0) = 0. (The initial velocity was unknown, and
Answer Preview: a First find v t by integrating a t Now integrate v t to find s t Since s t …

, Chapter: 13- The Trigonometric Functions -Problem: 9 >> Find each integral.?sin7 x cos x dx
Answer Preview: To find the integral of sin^7(x) * cos(x) dx, we can use a u-…

, Chapter: 1 -Problem: 54 >> A report estimated the cost to build a new 30% carbon sequestration coal-generated electricity plant with a capacity of 650 MW to be $3.308 billion, with a marginal cost of $7.17 for each MWh of electricity produced.(a) Find a formula for the cost, C(x), to build a plant and generate x MWh of electricity.(b) Calculate the total cost to generate 120 million MWh.(c) A region has $4.5 billion to spen
Answer Preview: a b The total cost to generate 120 milli…

, Chapter: 13 -Problem: 69 >> If a string with a fundamental frequency of 110 hertz is plucked in the middle, it will vibrate at the odd harmonics of 110, 330, 550,...hertz but not at the even harmonics of 220, 440, 660,...hertz. The resulting pressure P on the eardrum caused by the string can be approximated using the equationwhere P is in pounds per square foot at a time of t seconds after the string is plucked.(a) Graph P(t
Answer Preview: a Using the graphing calculator to graph in a 0 0 01 by 0 004 0 004 viewi…

, Chapter: 4 -Problem: 7 >> In Exercises 7–14, find f[g(x)] and g[f(x)].f(x) = x/8 + 7; g(x) = 6x – 1
Answer Preview: To find the compositions f g x and g f x you simply plug the expression for one function int…

, Chapter: 5 -Problem: 44 >> In Exercises, complete the following for each function. (a) Find intervals where the function is increasing or decreasing, and determine any relative extrema. (b) Find intervals where the function is concave upward or concave downward, and determine any inflection points. (c) Graph each function, considering the domain, critical points, symmetry, relative extrema, regions where the function is inc
Answer Preview: f is never zero a f x has no extrema Increasing …

, Chapter: 1 -Problem: 41 >> Use slopes to show that the quadrilateral with vertices at (1, 3), (-5/2, 2), (-7/2, 4), and (2, 1) is a parallelogram.
Answer Preview: A parallelogram has 4 sides with opposite sides parallel The slope of the line through 1 3 …

, Chapter: 3 -Problem: 85 >> Use a graphing calculator to graph the function. (a) Determine the limit from the graph. (b) Explain how your answer could be determined from the expression for f (x). Transcribed Image Text: lim X10 2 ?9x² + 5 2.x
Answer Preview: Graph the functions on a graphing calculator A go…

, Chapter: 4 -Problem: 17 >> Use the rules for derivatives to find the derivative of each function defined as follows. Transcribed Image Text: k(x) = 3x 4x + 7
Answer Preview: k x k x 3 x …

, Chapter: 5 -Problem: 102 >> A car rolls down a hill. Its distance (in feet) from its starting point is given by s(t) = 1.5t2 + 4t, where t is in seconds. (a) How far will the car move in 10 seconds? (b) What is the velocity at 5 seconds? At 10 seconds? (c) How can you tell from v(t) that the car will not stop? (d) What is the acceleration at 5 seconds? At 10 seconds? (e) What is happening to the velocity and the acceleration
Answer Preview: s t 1 5t 2 4t a The car will move 190 ft in 10 seconds b v t s t 3t 4 The veloc…

, Chapter: 9 -Problem: 72 >> The profit (in dollars) from selling x units of one product and y units of a second product is P = -(x - 100)2 - (y - 50)2 + 2000. The weekly sales for the first product vary from 100 units to 150 units, and the weekly sales for the second product vary from 40 units to 80 units. Estimate average weekly profit for these two products.
Answer Preview: P x y x 100 2 y …

, Chapter: 2 -Problem: 47 >> Consider the polynomial functions defined by ƒ(x) = (x - 1)(x - 2)(x + 3),  g(x) = x3 + 2x2 - x - 2, and h(x) = 3x3 + 6x2 - 3x - 6. (a) What is the value of ƒ(1)? (b) For what values, other than 1, is ƒ(x) = 0? (c) Verify that g(-1) = g(1) = g(-2) = 0. (d) Based on your answer from part (c), what do you think is the factored form of g(x)? Verify your answer by multiplying these factors and compari
Answer Preview: f x x 1 x 2 x 3 g x x 3 2x 2 x 2 h x 3x 3 6x 2 3x 6 a f 1 0 1 4 0 b …

, Chapter: 12 -Problem: 18 >> Use l’Hospital’s rule where applicable to find each limit. Transcribed Image Text: lim x-0 V9 + x - 3 X
Answer Preview: The limit in the numerator is 0 as is the l…

, Chapter: 1 -Problem: 41 >> Solve each quadratic inequality. Graph each solution.2x3 – 14x2 + 12x < 0
Answer Preview: To solve the quadratic inequality 2x 3 14x 2 12x 0 we ll start by factoring the expression on the left hand side and then analyzing the sign of the ex…

, Chapter: 8 -Problem: 45 >> The intensity of the reaction to a certain drug, in appropriate units, is given by R(t) = te-0.1t, where t is time (in hours) after the drug is administered. Find the average intensity during the following hours. (a) Second hour (b) Twelfth hour (c) Twenty-fourth hour
Answer Preview: R t te 0 1t During the nth hour corresponds to the interval n 1 n The averag…

, Chapter: 9 -Problem: 43 >> The time (in hours) that a branch of Amalgamated Entities needs to spend to meet the quota set by the main office can be approximated by T(x, y) = x4 + 16y4 - 32xy + 40, where x represents how many thousands of dollars the factory spends on quality control and y represents how many thousands of dollars they spend on consulting. Find the amount of money they should spend on quality control and on c
Answer Preview: Use substitution to solve the system of equations The critical points are 0 …

, Chapter: 7 -Problem: 54 >> Find the cost function for each marginal cost function.C?(x) = x + 1/x2; 2 units cost $5.50
Answer Preview: C x x 1 x 2 2 units cost 5 …

, Chapter: 7 -Problem: 30 >> Use substitution to find each indefinite integral. Transcribed Image Text: [4rV 4rV8 - r dr
Answer Preview: Let u 8 r so …

, Chapter: 13- The Trigonometric Functions -Problem: 25 >> Find each integral.?–6x cos 5x dx
Answer Preview: To find the integral of the function -6x cos(5x) dx, you can use integration by p…

, Chapter: 1 -Problem: 51 >> Use the formula for conversion between Fahrenheit and Celsius derived in Example 8 to convert each temperature.(a) 58°F to Celsius (b) -20°F to Celsius(c) 50°C to Fahrenheit
Answer Preview: Use the formula der…

, Chapter: 13 -Problem: 95 >> The body’s system of blood vessels is made up of arteries, arterioles, capillaries, and veins. The transport of blood from the heart through all organs of the body and back to the heart should be as efficient as possible. One way this can be done is by having large enough blood vessels to avoid turbulence, with blood cells small enough to minimize viscosity.We will find the value of angle 0 (see t
Answer Preview: a The sketch shows 0 in standard position From the d…

, Chapter: 5 -Problem: 28 >> For each function, find (a) The critical numbers; (b) The open intervals where the function is increasing;  (c) The open intervals where it is decreasing.f(x) = (x + 1)4/5
Answer Preview: To analyze the given function f x x 1 we ll need to find its critical numbers determine where it s i…

, Chapter: 5 -Problem: 23 >> In Exercises, complete the following for each function.(a) Find intervals where the function is increasing or decreasing, and determine any relative extrema. (b) Find intervals where the function is concave upward or concave downward, and determine any inflection points. (c) Graph each function, considering the domain, critical points, symmetry, relative extrema, regions where the function is incr
Answer Preview: Since f x does not exist when x 3 and x 3 the domain is 3 U 3 3 U 3 T…

, Chapter: 1 -Problem: 36 >> Suppose that the supply function for walnuts is p = S(q) = 0.25q + 3.6, where p is the price in dollars per pound and q is the quantity in bushels. Suppose also that the equilibrium price is $5.85, and the demand is 4 bushels when the price is $7.60. Find an equation for the demand function, assuming it is linear.
Answer Preview: Use the supply function to find the equilibrium quan…

, Chapter: 2 -Problem: 52 >> If b is the y-intercept of the graph of y = ƒ(x), what is the y-intercept of the graph of each of the following? (a) y = -ƒ(x) (b) y = ƒ(-x) (c) y = -ƒ(-x)
Answer Preview: a Since the graph of y f x is reflected vertically to obtain the graph of y f x the …

, Chapter: 4 -Problem: 19 >> In Exercises, find the derivative of each function. Transcribed Image Text: y || 6 x4 7 .3 X 3 + + ?5 X
Answer Preview: y dy dx 6 4 X 6x 4 6…

, Chapter: 5 -Problem: 79 >> Suppose a friend makes the following argument. A function ƒ is increasing and concave downward. Therefore, ƒ? is positive and decreasing, so it eventually becomes 0 and then negative, at which point ƒ decreases. Show that your friend is wrong by giving an example of a function that is always increasing and concave downward.
Answer Preview: There are many examples The easiest is f x x This graph is i…

, Chapter: 8 -Problem: 14 >> Determine whether each improper integral converges or diverges, and find the value of each that converges. Transcribed Image Text: Lax -00 -3 (x - 2)-³ dx
Answer Preview: The integral is convergent a…

, Chapter: 2 -Problem: 20 >> In Exercises, match the correct graph A–E to the function without using your calculator. Then, after you have answered all of them if you have a graphing calculator, use your calculator to check your answers. Each graph in this group is plotted on [-6, 6] by [-6, 6]. Transcribed Image Text: -6 6 -6
Answer Preview: The graph of y 2x 2 3 x 2 1 has the …

, Chapter: 12 -Problem: 32 >> Use Newton’s method to find the critical points for the functions defined as follows. Approximate them to the nearest hundredth. Decide whether each critical point leads to a relative maximum or a relative minimum.ƒ(x) = x3 + 9x2 - 6x + 4
Answer Preview: To find critical points solve so a solution exists in 7 6 Let c 1 7 Subsequent approximation…

, Chapter: 1 -Problem: 18 >> Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.4a2 + 10a + 6
Answer Preview: To factor the polynomial 4a 2 10a 6 we first look for common fact…

, Chapter: 8 -Problem: 35 >> Determine whether each improper integral converges or diverges, and find the value of each that converges. Transcribed Image Text: ["Cett, Ce-kt dt, k>0
Answer Preview: The integral is converg…

, Chapter: 9 -Problem: 45 >> The surface area of a human (in square meters) has been approximated by A = 0.024265h0.3964 m0.5378, where h is the height (in cm) and m is the mass (in kg). Find A for the following data.(a) Height, 178 cm; mass, 72 kg (b) Height, 140 cm; mass, 65 kg (c) Height, 160 cm; mass, 70 kg
Answer Preview: A 0 024265h 0 …

, Chapter: 6 -Problem: 56 >> The relationship between the number of species in a genus (x) and the number of genera (y) comprising x species is given by xya = k, where a and k are constants. Find dy/dx.
Answer Preview: X X dy dx aya 1 dy d…

, Chapter: 7 -Problem: 71 >> Exercises refer to Examples 9 and 10 in this section.For a particular object, a(t) = 5t2 + 4 and v(0) = 6. Find v(t). Examples 9 Suppose the velocity of an object at time t is v(t) = 6t2 - 8t and that the object is at 5 when time is 0. Find s(t), the function that gives the position of the object at time t.
Answer Preview: a t v t v 0 5t 4 …

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, Chapter: 1 -Problem: 32 >> Find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ? 0.Through (0, 5), perpendicular to 8x + 5y = 3
Answer Preview: Through 0 5 perpendicular to 8x …

, Chapter: 13 -Problem: 65 >> Graph each function, considering the domain, critical points, symmetry, relative extrema, regions where the function is increasing or decreasing, inflection points, and regions where the function is concave upward or concave downward.ƒ(x) = x - sin x
Answer Preview: Since f x is positive except at the isolated points x 2n for i…

, Chapter: 4 -Problem: 5 >> Determine whether each of the following statements is true or false, and explain why.The chain rule is used to take the derivative of a product of functions.
Answer Preview: True The chain rule is a fundamental concept in calculus that is used to find the derivative of …

, Chapter: 5 -Problem: 21 >> Find the open intervals where f is increasing or decreasing. Transcribed Image Text: f(x) = 16 9 - 3x
Answer Preview: f x 0 for all x x 3 and f …

, Chapter: 1 -Problem: 24 >> An Internet site for downloading music charges a $10 registration fee plus 99 cents per downloaded song. Write a linear cost function for each situation. Identify all variables used.
Answer Preview: 10 is the fixed cost and 0 99 is the cost per …

, Chapter: 2 -Problem: 51 >> If r is an x-intercept of the graph of y = ƒ(x), what is an x-intercept of the graph of each of the following?(a) y = -ƒ(x) (b) y = ƒ(-x) (c) y = -ƒ(-x)
Answer Preview: a Since the graph of y f x is reflected vertically to obtain the graph of y f x the …

, Chapter: 4 -Problem: 86 >> The length of the monkeyface prickleback, a West Coast game fish, can be approximated by L = 71.5(1 - e-0.1t) and the weight by W = 0.01289 • L2.9, where L is the length in centimeters, t is the age in years, and W is the weight in grams. (a) Find the approximate length of a 5-year-old monkeyface. (b) Find how fast the length of a 5-year-old monkeyface is growing. (c) Find the approximate weight o
Answer Preview: a L 5 71 5 1 e 0 5 28 1 The approximate length of a 5 year old monkey fa…

, Chapter: 5 -Problem: 96 >> Researchers used a version of the Gompertz curve to model the growth of breast cancer tumors with the equation N(t) = ec(1-e-kt), where N(t) is the number of cancer cells after t days, c = 27.3, and k = 0.011. Find the inflection point and describe what it signifies.
Answer Preview: Letting c 27 3 and k 0 011 Verify that there is a point of inflec…

, Chapter: 9 -Problem: 75 >> We saw that the profit (in thousands of dollars) that Aunt Mildred’s Metalworks earns from producing x tons of steel and y tons of aluminum can be approximated by P(x, y) = 36xy - x3 - 8y3. If the amount of steel produced varies from 0 to 8 tons, and the amount of aluminum produced varies from 0 to 4 tons, find the average profit.
Answer Preview: P x y 36xy x 3 8y 3 Areas 8 0 …

, Chapter: 2 -Problem: 39 >> Suppose logb 2 = a and logb 3 = c. Use the properties of logarithms to find the following. logb (72b)
Answer Preview: log b 72b log b 72 lo…

, Chapter: 12 -Problem: 15 >> For the functions defined as follows, find the Taylor polynomials of degree 4 at 0.ƒ(x) = ln(1 - x)
Answer Preview: f x ln 1 x 1 1 X x x 1 x Derivative x 2 …

, Chapter: 1 -Problem: 16 >> Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.6a2 – 48a – 120
Answer Preview: To factor the polynomial 6a 2 48a 120 we can start by factoring out the greatest …

, Chapter: 8 -Problem: 3 >> Integration by parts cannot be used on a definite integral.Determine whether each statement is true or false, and explain why.
Answer Preview: False Integr…

, Chapter: 9 -Problem: 64 >> Give an example of a region that cannot be expressed by either of the forms shown in Figure 6. Transcribed Image Text: 0 a y=h(x) y = g(x) g(x) = h(x) for all x in [a, b] (a) d 0 Figure 6 x = g(y) x=h(y) g(y) h(y) for all y in [c, d] (b) X
Answer Preview: The region representing the center of the earth is not expres…

, Chapter: 6 -Problem: 54 >> Suppose the demand function for a product is given by q = A/pk, where A and k are positive constants. For what values of k is the demand elastic? Inelastic?
Answer Preview: The demand is elastic …

, Chapter: 7 -Problem: 29 >> Use substitution to find each indefinite integral. Transcribed Image Text: [P(P p(p + 1)5 dp
Answer Preview: Let u p 1 …

, Chapter: 13- The Trigonometric Functions -Problem: 72 >> Find each integral.?x2 sin 4x3 dx
Answer Preview: To find the integral of x^2 * sin(4x^3) dx, we can use integration by s…

, Chapter: 1 -Problem: 36 >> An interesting phenomenon occurred with the 2000 New York Yankees. The following table shows the number of base hits, triples, and home runs for those Yankees with at least 300 at-bats.(a) Find the correlation coefficient between the number of hits and the number of triples.(b) Find the correlation coefficient between the number of hits and the number of home runs.(c) Given the positive correlatio
Answer Preview: a Use a calculators statistical features to obtain the correlation coefficient betwee…

, Chapter: 13 -Problem: 29 >> Find each function value without using a calculator. Transcribed Image Text: sin 6
Answer Preview: When an angle of 6 is dr…

, Chapter: 5 -Problem: 31 >> For each function, find (a) The critical numbers; (b) The open intervals where the function is increasing;  (c) The open intervals where it is decreasing.f(x) = xe–3x
Answer Preview: To find the critical numbers increasing intervals and decreasing intervals for the given function f …

, Chapter: 5 -Problem: 40 >> In Exercises, complete the following for each function. (a) Find intervals where the function is increasing or decreasing, and determine any relative extrema. (b) Find intervals where the function is concave upward or concave downward, and determine any inflection points. (c) Graph each function, considering the domain, critical points, symmetry, relative extrema, regions where the function is inc
Answer Preview: Domain is The graph has no symmetry a Rel…

, Chapter: 1 -Problem: 29 >> Assume that each situation can be expressed as a linear cost function. Find the cost function in each case.Marginal cost: $75; 50 items cost $4300 to produce.
Answer Preview: Marginal cost 75 50 ite…

, Chapter: 4 -Problem: 85 >> Suppose a population is growing logistically with k = 5 * 10-6, m = 30,000, and G0 = 2000. Assume time is measured in years. (a) Find the growth function G(t) for this population. (b) Find the population and rate of growth of the population after 6 years. Interpret your results.
Answer Preview: m 30 000 G o 2000 and k …

, Chapter: 5 -Problem: 5 >> By sketching a graph of the function or by investigating values of the function near 0, find limxx?? The calculator shows no y-value when x = 0  because 0 is not in the domain of this function. However, we see from the graph that 0 = In |x|.
Answer Preview: Graph y x ln x on a graphing calculator A suitable …

, Chapter: 8 -Problem: 9 >> Find the volume of the solid of revolution formed by rotating about the x-axis each region bounded by the given curves. Transcribed Image Text: f(x) = 1 x + 2, y = 0, x = 1, x = 3 3
Answer Preview: f x x 2 y 0 x 1 x 3 3 y …

, Chapter: 2 -Problem: 45 >> Solve each equation in Exercises. Round decimal answers to four decimal places.logx 36 = -2
Answer Preview: log 36 …

, Chapter: 12 -Problem: 33 >> Find the payments necessary to amortize each loan.$55,000, 6% compounded monthly, 36 monthly payments
Answer Preview: 55 000 is the present value of this …

, Chapter: 1 -Problem: 13 >> Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.12x2 – 5x = 2
Answer Preview: To solve the quadratic equation 12x 2 5x 2 we can rear…

, Chapter: 7 -Problem: 20 >> In Exercises, find each indefinite integral. Transcribed Image Text: (5x - 1) dx
Answer Preview: S 5 …

, Chapter: 9 -Problem: 63 >> A weight-loss counselor has prepared a program of diet and exercise for a client. If the client sticks to the program, the weight loss that can be expected (in pounds per week) is given bywhere c is the average daily calorie intake for the week and n is the number of 40-minute aerobic workouts per week.(a) How many pounds can the client expect to lose by eating an average of 1200 cal per day and p
Answer Preview: a The client could expect to lose 4 125 lb b …

, Chapter: 7 -Problem: 48 >> Find the area of each shaded region. Transcribed Image Text: 0 -2 -4 1 y = +2 2 In x X e 3 X
Answer Preview: From the gra…

, Chapter: 7 -Problem: 44 >> In Exercises, use the definite integral to find the area between the x-axis and f(x) over the indicated interval. Check first to see if the graph crosses the x-axis in the given interval. Transcribed Image Text: ?(x) = 1 - 1 ; [e ¹, e] X
Answer Preview: The graph crosses the x a…

, Chapter: 13- The Trigonometric Functions -Problem: 38 >> Find each function value.cos 72°
Answer Preview: To find the value of the cosine of 72 degrees (cos 72), you can use a calculator or tr…

, Chapter: 1 -Problem: 32 >> The following data give the expected points for a football team with first down and 10 yards to go from various points on the field.(a) Calculate the correlation coefficient. Does there appear to be a linear correlation? (b) Find the equation of the least squares line. (c) Use your answer from part (a) to predict the expected points when a team is at the 50-yd line.
Answer Preview: a b c Let x 50 Y 0 0769 50 5 91 2 07 The predic…

, Chapter: 13 -Problem: 28 >> Find each integral. Transcribed Image Text: fr sec x5 tan x5 dx
Answer Preview: Sx sec x tanxdx Let u x so …

, Chapter: 4 -Problem: 4 >> Determine whether each of the following statements is true or false, and explain why.The marginal cost function is the derivative of the cost function.
Answer Preview: The statement is true The marginal cost function is indeed the derivative …

, Chapter: 5 -Problem: 30 >> Find the locations and values of all relative maxima and minima.ƒ(x) = 2x3 + 3x2 - 12x + 5
Answer Preview: Critical numbers 2 1 f x 12x 6 f 2 18 0 so a ma…

, Chapter: 1 -Problem: 20 >> Find the slope for each line that has a slope.4x - y = 7
Answer Preview: 4x y…

, Chapter: 4 -Problem: 21 >> Find the derivative of each function. Transcribed Image Text: y In x 4x + 7
Answer Preview: Use th…

, Chapter: 5 -Problem: 57 >> In Exercises, complete the following for each function. (a) Find intervals where the function is increasing or decreasing, and determine any relative extrema. (b) Find intervals where the function is concave upward or concave downward, and determine any inflection points. (c) Graph each function, considering the domain, critical points, symmetry, relative extrema, regions where the function is inc
Answer Preview: f x 4x 1 3 x 4 3 Domain is f x 4 x 1 3 x 4 3 4x 1 3 x …

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, Chapter: 2 -Problem: 31 >> In Exercises, find any horizontal and vertical asymptotes and any holes that may exist for each rational function. Draw the graph of each function, including any x- and y-intercepts. Transcribed Image Text: y = -4 x + 2
Answer Preview: The function is undefined for x 2 so the line …

, Chapter: 12 -Problem: 17 >> Find a5 and an for the following geometric sequences.a4 = 64, r = -4
Answer Preview: a 4 64 r 4 To find a use a 4 …

, Chapter: 1 -Problem: 13 >> Using the variable x, write each interval as an inequality. Transcribed Image Text: -4 0 4
Answer Preview: In interval notation 4 4 represents all real numbers between 4 and 4 excluding …

, Chapter: 8 -Problem: 50 >> Find the capital value of an asset that generates $7200 yearly income if the interest rate is as follows. (a) 5% compounded continuously (b) 10% compounded continuously
Answer Preview: a The integral converges The capital value is …

, Chapter: 9 -Problem: 41 >> Find fxx(x, y) and fxy(x, y).ƒ(x, y) = 4x2e2y
Answer Preview: f x y 4xey…

, Chapter: 7 -Problem: 62 >> An oil tanker is leaking oil at the rate given (in barrels per hour) bywhere t is the time (in hours) after the tanker hits a hidden rock (when t = 0).(a) Find the total number of barrels that the ship will leak on the first day. (b) Find the total number of barrels that the ship will leak on the second day. (c) What is happening over the long run to the amount of oil leaked per day?
Answer Preview: The tanker is leaking oil at a rate in barrels per hour of a Let u ln t 1 so t…

, Chapter: 7 -Problem: 33 >> On March 13, 2020, President Trump signed a proclamation declaring that the COVID-19 outbreak in the U. S. constituted a national emergency. Sweeping changes were made throughout the nation, including social distancing, in an effort to control the spread of the virus. The graph on the next page gives the number of daily new cases of COVID-19 in the U.S. for 30 days following the proclamation. Esti
Answer Preview: Left endpoints Read values of the function on the gr…

, Chapter: 13- The Trigonometric Functions -Problem: 20 >> Convert the following degree measures to radians. Leave answers as multiples of ?.405°
Answer Preview: To convert degrees to radians, you can use the conversion facto…

, Chapter: 1 -Problem: 49 >> Deer ticks are of concern because they can carry the parasite that causes Lyme disease. One study found a relationship between the density of acorns produced in the fall and the density of deer tick larvae the following spring. The relationship can be approximated by the linear function ƒ(x) = 34x + 230, where x is the number of acorns per square meter in the fall, and ƒ(x) is the number of deer t
Answer Preview: a Approximately 23 acorns per square meter would produce 1000 de…

, Chapter: 13 -Problem: 74 >> Graph each function defined in Exercises over a twoperiod interval.y = -sin x
Answer Preview: The graph of y sin x is …

, Chapter: 4 -Problem: 2 >> Apply Equation (1) to the voltage of a point charge (Equation (4)) to obtain the electric field of a point charge (Equation (5)). Equations Transcribed Image Text: E = d? dz' (1)
Answer Preview: Given function Voltage …

, Chapter: 5 -Problem: 25 >> In Exercises, find ƒ??(x), the third derivative of ƒ, and ƒ(4)(x), the fourth derivative of ƒ, for each function.ƒ(x) = 5x5 - 3x4 + 2x3 + 7x2 + 4
Answer Preview: f x 5x 3x 2x 7x 4 …

, Chapter: 1 -Problem: 28 >> In exercises, find an equation in slope-intercept form for each line.Through 1-1, 32 and 10, 32
Answer Preview: The line goes through 1 3 a…

, Chapter: 4 -Problem: 15 >> Find the derivative of each function.y = -5x ln(3x + 2)
Answer Preview: y 5x ln 3x 2 Use the …

, Chapter: 5 -Problem: 98 >> Researchers have developed a mathematical model that can be used to estimate the number of teeth N(t) at time t (days of incubation) for Alligator mississippiensis, where N(t) = 71.8e-8.96e-0.0685t. Find the inflection point and describe its importance to this research.
Answer Preview: N t has an inflection point at 32 01 N 32 01 …

, Chapter: 8 -Problem: 10 >> Determine whether each improper integral converges or diverges, and find the value of each that converges. Transcribed Image Text: -4 3 -00 x 4 dx
Answer Preview: S 3 As a dx lim a11x S 3 3 …

, Chapter: 2 -Problem: 37 >> Given the following graph, sketch by hand the graph of the function described, giving the new coordinates for the three points labeled on the original graph. Transcribed Image Text: t (-1,4) (-3,-2) 0 X (5,0)
Answer Preview: The graph of y …

, Chapter: 12 -Problem: 13 >> Find a4 and an for the following geometric sequences. Then find the sum of the first five terms.a1 = 5, r = -2
Answer Preview: al 7 3 5 2 …

, Chapter: 8 -Problem: 3 >> The present value of money flow for T years is the integral from 0 to T of the function giving the rate of money flow.Determine whether each statement is true or false, and explain why.
Answer Preview: False The present value of …

, Chapter: 9 -Problem: 57 >> Find positive numbers x and y, whose sum is 75, such that xy2 is maximized.
Answer Preview: Maximize f x y xy 2 subject to x y 75 Equations 1 and 2 give y…

, Chapter: 6 -Problem: 53 >> A hunter is at a point along a river bank. He wants to get to his cabin, located 3 miles north and 8 miles west. (See the figure.) He can travel 5 mph along the river but only 2 mph on this very rocky land. How far upriver should he go in order to reach the cabin in minimum time? Transcribed Image Text:
Answer Preview: Let 8 x the distance the hunter will travel on the river Th…

, Chapter: 7 -Problem: 47 >> A worker sketches the curves y = ?x and y = x/2 on a sheet of metal and cuts out the region between the curves to form a metal plate. Find the area of the plate.
Answer Preview: To find the poi…

, Chapter: 10 -Problem: 1 >> Kimberly Austin deposits $5000 in an IRA at 6% interest compounded continuously for her retirement in 10 years. She intends to make continuous deposits at the rate of $3000 a year until she retires. How much will she have accumulated at that time?
Answer Preview: To calculate how much Kimberly will have accumulated in her IRA after 10 years with continuous depos…

, Chapter: 1 -Problem: 55 >> The cost function for flavored coffee at an upscale coffeehouse is given in dollars by C(x) = 3x + 160, where x is in pounds. The coffee sells for $7 per pound. (a) Find the break-even quantity. (b) What will the revenue be at that point?
Answer Preview: a The break even quantity i…

, Chapter: 13 -Problem: 78 >> Graph each function defined in Exercises over a twoperiod interval. Transcribed Image Text: y || 1 2 tan x
Answer Preview: The graph of y 1 2tan x is similar to the graph of y tan x excep…

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, Chapter: 5 -Problem: 24 >> In Exercises, complete the following for each function.(a) Find intervals where the function is increasing or decreasing, and determine any relative extrema. (b) Find intervals where the function is concave upward or concave downward, and determine any inflection points. (c) Graph each function, considering the domain, critical points, symmetry, relative extrema, regions where the function is incr
Answer Preview: Since f x does not exist when x 2 and x 2 the domain is 2 U 2 2 U 2 The graph is symmetric a…

, Chapter: 1 -Problem: 16 >> The number of nonmobile broadband subscriptions per 100 inhabitants of the U.S. in recent years is given in the following table.(a) Find an equation for the least squares line, letting x be the number of years since 2000.(b) Based on your answer to part (a), at approximately what rate is the number of subscriptions per 100 inhabitants growing per year?(c) Use your result from part (a) to predict t
Answer Preview: a b The number of subscriptions is growing at a rate of …

, Chapter: 4 -Problem: 49 >> Use the rules for derivatives to find the derivative of each function defined as follows.ƒ(x) = e2x ln(xex + 1)
Answer Preview: x e 2x ln xe x 1 Us…

, Chapter: 5 -Problem: 103 >> If a cannonball is shot directly upward with a velocity of 256 ft per second, its height above the ground after t seconds is given by s(t) = 256t - 16t2. Find the velocity and the acceleration after t seconds. What is the maximum height the cannonball reaches? When does it hit the ground?
Answer Preview: To find when the maximum height occurs set Find …

, Chapter: 8 -Problem: 11 >> Use integration by parts to find the integrals in Exercises. Transcribed Image Text: 2x + 1 ox dx
Answer Preview: 2x 1 5x 1dx 0 et 1 f x 2x 1 ex dx Le…

, Chapter: 2 -Problem: 32 >> In Exercises, follow the directions for. y = ?-x - 2 - 4 Transcribed Image Text: -10 -10 -10 10 -10 (A) 10 -10 (C) 10 -10 (E) 10 10 10 -10 -10 -10 10 -10 (B) 10 -10 (D) 10 -10 (F) 10 10 10
Answer Preview: The graph of y x 2 4 is the same as …

, Chapter: 12 -Problem: 14 >> Identify which geometric series converge. Give the sum of each convergent series. Transcribed Image Text: 4 5 + 25 + 5 +
Answer Preview: is a geometric serie…

, Chapter: 1 -Problem: 32 >> Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.16a4 – 81b4
Answer Preview: The given polynomial is 16a 4 81b 4 This is a diff…

, Chapter: 8 -Problem: 34 >> Find the average value of each function on the given interval.ƒ(x) = x ln x; [1, e]
Answer Preview: x x ln x 1 e Use c…

, Chapter: 7 -Problem: 62 >> The marginal profit of a small fast-food stand is given, in thousands of dollars, bywhere x is the sales volume in thousands of hamburgers. The “profit” is -$1000 when no hamburgers are sold. Find the profit function. Transcribed Image Text: P'(x) = ?x + 12/?
Answer Preview: profit is …

, Chapter: 7 -Problem: 70 >> The average annual increment in the horn length (in centimeters) of bighorn rams born in recent years can be approximated by y = 0.1762x2 - 3.986x + 22.68, where x is the ram’s age (in years) for x between 3 and 9. Integrate to find the total increase in the length of a ram’s horn during this time.
Answer Preview: The total increase in the length o…

, Chapter: 13- The Trigonometric Functions -Problem: 6 >> Find the derivatives of the functions defined as follows.y = –9 sin5 x
Answer Preview: To find the derivative of the function y = -9sin^5(x), you can use …

, Chapter: 13 -Problem: 62 >> Use a calculator to find the following function values.tan 54°
Answer Preview: ta…

, Chapter: 4 -Problem: 14 >> In Exercises 7–14, find f[g(x)] and g[f(x)]. Transcribed Image Text: 8 f(x) = — ; g(x) = ?3-x X
Answer Preview: Given x 8 …

, Chapter: 5 -Problem: 41 >> In Exercises, complete the following for each function. (a) Find intervals where the function is increasing or decreasing, and determine any relative extrema. (b) Find intervals where the function is concave upward or concave downward, and determine any inflection points. (c) Graph each function, considering the domain, critical points, symmetry, relative extrema, regions where the function is inc
Answer Preview: Domain is The graph has no symmetry Critical numbers 0 2 …

, Chapter: 1 -Problem: 3 >> Determine whether each statement is true or false, and explain why.The line y = -2x + 5 intersects the point (3, -1).
Answer Preview: True The poin…

, Chapter: 4 -Problem: 67 >> In Exercise 48 in Section 4.2, we saw an example for which the erroneous version of the product rule, [ƒ(x)g(x)]?= ƒ?(x)g?(x), does hold. As a more general version of this example, calculate [ƒ(x)g(x)]?and ƒ?(x)g?(x) for ƒ(x) = a/(n - x)n and g(x) = bxn for n ? 0, and verify that they are equal. Data from Exercise 48 in Section 4.2There are special cases in which the derivative of ƒ(x)g(x) does eq
Answer Preview: Let f x a n x and g x bx for n 0 x g x …

, Chapter: 5 -Problem: 48 >> In Exercises, complete the following for each function. (a) Find intervals where the function is increasing or decreasing, and determine any relative extrema. (b) Find intervals where the function is concave upward or concave downward, and determine any inflection points. (c) Graph each function, considering the domain, critical points, symmetry, relative extrema, regions where the function is inc
Answer Preview: f x 6x3 x4 Domain is The graph has no symmetry f x 18x 2 4x 3 2x 2 9 2x …

, Chapter: 10 -Problem: 41 >> Suppose that 0 < y0 < N. Let b = (N - y0)/y0 , and let y(x) = N/(1 + be-kx) for all x. Show the following. (a) 0 < y(x) < N for all x. (b) The lines y = 0 and y = N are horizontal asymptotes of the graph. (c) y(x) is an increasing function. (d) ((ln b)/k, N/2) is a point of inflection of the graph. (e) dy/dx is a maximum at x0 = (ln b)/k.
Answer Preview: a 0 y 0 N implies that y 0 0 N 0 and N y 0 0 Therefore Al…

, Chapter: 9 -Problem: 90 >> The cost (in dollars) to manufacture x solar cells and y solar collectors is c(x, y) = x2 + 5y2 + 4xy - 70x - 164y + 1800. (a) Find values of x and y that produce minimum total cost. (b) Find the minimum total cost.
Answer Preview: a Minimize c x y Extremum at 11 12 c xx …

, Chapter: 2 -Problem: 19 >> Solve equation.3x = 1/81
Answer Preview: 3 x 1 …

, Chapter: 12 -Problem: 16 >> Use l’Hospital’s rule where applicable to find each limit. Transcribed Image Text: lim x?0 8x5 et 3x4
Answer Preview: and lHospi…

, Chapter: 1 -Problem: 11 >> Solve each equation by factoring or by using the quadratic formula. If the solutions involve square roots, give both the exact solutions and the approximate solutions to three decimal places.m2 = 14m – 49
Answer Preview: To solve the equation m 2 14m 49 we can follow these steps Move all t…

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, Chapter: 6 -Problem: 57 >> A simple biochemical reaction with three molecules has solutions that oscillate toward a steady state when positive constants a and b are below the curve b - a = (b + a)3. Find the largest possible value of a for which the reaction has solutions that oscillate toward a steady state.
Answer Preview: b a b a d db da db b a 1 v 9 v da db da db …

, Chapter: 7 -Problem: 26 >> Find the area between the curves in Exercises.y = ?x, y = x?x
Answer Preview: y x y x x To find the points of in…

, Chapter: 12- Sequences and Series -Problem: 41 >> Rebecca Nasman sells some land in Nevada. She will be paid a lump sum of $60,000 in 7 years. Until then, the buyer pays 8% interest, compounded quarterly.a. Find the amount of each quarterly interest payment.b. The buyer sets up a sinking fund so that enough money will be present to pay off the $60,000. The buyer wants to make semiannual payments into the sinking fund; the account pays 6% compound
Answer Preview: Let's break down each part of the problem: a. Find the amount of each quarterly interest payment. To find the amount of each quarterly interest paymen…

, Chapter: 13 -Problem: 84 >> Find each integral. Transcribed Image Text: x tan 11x² dx
Answer Preview: frt x tan 11x dx Let u 11x …

, Chapter: 4 -Problem: 15 >> Find the derivative of each function defined as follows.p(x) = –10x–1/2 + 8x–3/2
Answer Preview: To find the derivative of the function p x 10x 8a we wil…

, Chapter: 5 -Problem: 21 >> In Exercises, complete the following for each function.(a) Find intervals where the function is increasing or decreasing, and determine any relative extrema. (b) Find intervals where the function is concave upward or concave downward, and determine any inflection points. (c) Graph each function, considering the domain, critical points, symmetry, relative extrema, regions where the function is incr
Answer Preview: Domain is The graph is symmetric about the origin Critical numbers …

, Chapter: 1 -Problem: 9 >> Consider the following table of data.(a) Calculate the least squares line and the correlation coefficient.(b) Repeat part (a), but this time delete the last point.(c) Draw a graph of the data, and use it to explain the dramatic difference between the answers to parts (a) and (b). Transcribed Image Text:
Answer Preview: a b c The point 9 9 is an outlier that …

, Chapter: 4 -Problem: 83 >> The U.S. dollar has been declining in value over the last century, except during the Great Depression, when it increased in value. The following table shows the number of dollars it took in various years to equal $1 in 1913.(a) Using the regression feature on a graphing calculator, find a cubic function that models these data, letting t = 0 correspond to the year 1900. (b) Using your answer to par
Answer Preview: a Using the regression feature on a graphing calculator a cubic function that …

, Chapter: 5 -Problem: 58 >> In Exercises, find the open intervals where the functions are concave upward or concave downward. Find any inflection points.ƒ(x) = 5-x2
Answer Preview: Concave upward on an…

, Chapter: 10 -Problem: 41 >> The lifetime of a printer costing $200 is exponentially distributed with mean 2 years. The manufacturer agrees to pay a full refund to a buyer if the printer fails during the first year following its purchase, and a one-half refund if it fails during the second year. If the manufacturer sells 100 printers, how much should it expect to pay in refunds? Choose one of the following.(a) 6321 (b) 7358 (
Answer Preview: Let the random variable X be the lifetime of the printer in a years Then it has exponential distri…

, Chapter: 9 -Problem: 74 >> In 1931, Albert Einstein developed the following formula for the sum of two velocities, x and y:where x and y are in miles per second and c represents the speed of light, 186,282 miles per second.(a) Suppose that, relative to a stationary observer, a new super space shuttle is capable of traveling at 50,000 miles per second and that, while traveling at this speed, it launches a rocket that travels
Answer Preview: a The rocket is traveling 164 500 m s…

, Chapter: 2 -Problem: 29 >> Solve equation.5x2+x = 1
Answer Preview: gr tr 5 1 …