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Chapter: 2 -Problem: 9 >> In Exercises 1 through 12, use the chain rule to compute the derivative dy/dx and simplify your answer.y = u2 + 2u ? 3; u = ?x
Answer Preview: y u 2u 3 u x x 2 d…

, Chapter: 6 -Problem: 4 >> In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. Transcribed Image Text: 1 -00 -2/3 X dx
Answer Preview: I S0 x X …

, Chapter: 5 -Problem: 37 >> Answer the questions in Exercise 36 for a country whose life expectancy function is Data from Exercises 36 In a certain undeveloped country, the life expectancy of a person t years old is L(t) years, where L(t) = 41.6(1 + 1.07t)0.13 a. What is the life expectancy of a person in this country at birth? At age 50? b. What is the average life expectancy of all people in this country between the ages
Answer Preview: a At birth b c To find the age T such that L T T we must …

, Chapter: 3 -Problem: 38 >> Dan wants to use 300 meters of fencing to surround two identical adjacent rectangular plots, as shown in the accompanying figure. How should he do this to make the combined area of the plots as large as possible? Transcribed Image Text: HHH 7 O
Answer Preview: Let y be the length of the shared piece of fencing and x the length of the other side of either re…

, Chapter: 7 -Problem: 1 >> In Exercises 1 through 10, find the partial derivatives fx and fy. Transcribed Image Text: f(x, y) = 2x³y + 3xy² + y X
Answer Preview: y f x y …

, Chapter: 8 -Problem: 52 >> In Exercises 43 through 76, simplify the given expression as much as possible. Assume a, b, and c are positive real numbers. Transcribed Image Text: 3?-3 2c -212 a³
Answer Preview: To simplify the expression let s break it down step by step Starting with the first term 3a 3 c 2 1 …

, Chapter: 5 -Problem: 47 >> In Exercises 47 through 50, use an appropriate substitution to solve the given separable differential equation. Transcribed Image Text: dy dx 2-y (x + 1)²
Answer Preview: dy 2 y dx x 1 Cross multiplying gives x 1 dy 2 y dx Multiplying both sides by …

, Chapter: 5 -Problem: 23 >> In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. Transcribed Image Text: Sex(4- 10 e *(4- e¹) dx
Answer Preview: L ex e 4 …

, Chapter: 7 -Problem: 38 >> In Exercises 37 through 44, sketch the region of integration for the given integral and set up an equivalent integral with the order of integration reversed. Transcribed Image Text: 2y SS 0 f(x, y) dx dy
Answer Preview: Using vertical cros…

, Chapter: 3 -Problem: 33 >> When a particular commodity is priced at p dollars per unit, consumers demand q units, where p and q are related by the equation q2 + 3pq = 22.a. Find the elasticity of demand for this commodity.b. For a unit price of $3, is the demand elastic, inelastic, or of unit elasticity?
Answer Preview: q 2 3pq 22 a Using implicit differentiation …

, Chapter: 5 -Problem: 11 >> In Exercises 1 through 20, find the indicated indefinite integral. Transcribed Image Text: fox (x + 2)(x² + 4x + 2)5 dx
Answer Preview: x 2 x 4x 2 5 dx Let …

, Chapter: 2 -Problem: 62 >> Find h'(?1) if g(?1) = ?1 and g'(?1) = 1, where h(x) = [3g2(x) + 4g(x) + 2]5 [g(x) + x].
Answer Preview: h x 3g x 4g x 2 g x x H x 3g x 4g x 2 g x x g x x 3g x …

, Chapter: 4 -Problem: 27 >> The economics editor at a major publishing house estimates that if x thousand complimentary copies are distributed to professors, the first-year sales of a certain new text will be f(x) = 15 ? 20e?0.3x thousand copies. Currently, the editor is planning to distribute 9,000 complimentary copies.a. Use marginal analysis to estimate the increase in first-year sales that will result if 1,000 additional
Answer Preview: f x 15 20e 0 3x a f f x where x is the current number of compli…

, Chapter: 2 -Problem: 14 >> In Exercises 13 through 20, use the chain rule to compute the derivative dy/dx for the given value of x. Transcribed Image Text: 1 yu+u = 5 2x for x = 0 = ? -
Answer Preview: 1 y u u u U u u dy du …

, Chapter: 3 -Problem: 45 >> A national consumers’ association determines that x years after its founding in 1998, it will have P(x) members, whereP(x) = 100(2x3 ? 45x2 + 264x)a. At what time between 2000 and 2013 was the membership largest? Smallest?b. What were the largest and smallest membership levels between 2008 and 2013?
Answer Preview: P x 100 2x 3 45x 2 264x a The period of time between 2000 and 2013 corresponds to …

, Chapter: 6 -Problem: 13 >> In Exercises 11 through 18, either find a number k such that the given function is a probability density function or explain why no such number exists. Transcribed Image Text: f(x) = [(kx - 1)(x-2) for 0?x? 2 to otherwise
Answer Preview: But using this k can find a value for …

, Chapter: 5 -Problem: 35 >> In Exercises 3 through 36, find the indicated integral and check your answer by differentiation. Transcribed Image Text: 1 ?x(?x + 1) dx
Answer Preview: Let u x 1 Then du dx …

, Chapter: 3 -Problem: 37 >> Gina manages a company that makes toys. Her firm produces an inexpensive doll (Floppsy) and an expensive doll (Moppsy) in units of x hundreds and y hundreds, respectively. Gina finds that it is possible to produce the dolls in such a way that for 0 ? x ? 8 and that the company receives twice as much for selling a Moppsy doll as for a Floppsy doll. How many units of each kind of doll (both x and
Answer Preview: The relationship between the number of Moppsy dolls and Floppsy dolls is given by with the …

, Chapter: 7 -Problem: 10 >> In Exercises 1 through 16, compute the indicated functional value.f(x, y) = xyexy; f(1, ln 2), f(ln 3, ln 4)
Answer Preview: f x y xyey 1 In 2 l…

, Chapter: 8 -Problem: 57 >> In Exercises 43 through 76, simplify the given expression as much as possible. Assume a, b, and c are positive real numbers. Transcribed Image Text: 655836
Answer Preview: We are given the expression 3 6 5 5 8 3 6 and we need to sim…

, Chapter: 5 -Problem: 45 >> A tumor has approximately the same shape as the solid formed by rotating the region under the curve about the x axis, where x and y are measured in centimeters. Use integration to estimate the volume of the tumor. Transcribed Image Text: y = ?x(3 - x)
Answer Preview: y x 3 x 3x 1 2 x 3 2 The graph of y crosses …

, Chapter: 5 -Problem: 30 >> In Exercises 29 through 34, find the Gini index for the given Lorenz curve.L(x) = x2
Answer Preview: L x x2 G …

, Chapter: 7 -Problem: 40 >> In Exercises 37 through 44, sketch the region of integration for the given integral and set up an equivalent integral with the order of integration reversed. Transcribed Image Text: 5.1² Jy/2 f(x, y) dx dy
Answer Preview: Using vertical cross …

, Chapter: 3 -Problem: 33 >> Homing pigeons will rarely fly over large bodies of water unless forced to do so, presumably because it requires more energy to maintain altitude in flight in the heavy air over cool water. Suppose a pigeon is released from a boat B floating on a lake 5 miles from a point A on the shore and 13 miles from the pigeon’s loft L, as shown in the accompanying figure. Assuming the pigeon requires twice a
Answer Preview: Let x be the distance along the shoreline from A to P Then the distance from B to P is th…

, Chapter: 4 -Problem: 58 >> How much should you invest now at an annual interest rate of 6.25% so that your balance 10 years from now will be $2,000 if interest is compounded:a. Monthlyb. Continuously
Answer Preview: a Using the present value formula …

, Chapter: 5 -Problem: 11 >> In Exercises 7 through 14, find the volume of the solid formed by rotating the region R about the x axis. R is the region under the curve from x = ? 2 to x = 2. Transcribed Image Text: y = ?4 = x²
Answer Preview: Volume of S T 1 …

, Chapter: 2 -Problem: 72 >> The product rule tells you how to differentiate the product of any two functions, while the constant multiple rule tells you how to differentiate products in which one of the factors is constant. Show that the two rules are consistent. In particular, use the product rule to show that if c is a constant. Transcribed Image
Answer Preview: d dx df d…

, Chapter: 4 -Problem: 9 >> In Exercises 7 through 14, find all real numbers x that satisfy the given equation.4 ln x = 8
Answer Preview: 4 ln x …

, Chapter: 2 -Problem: 11 >> In Exercises 1 through 18, differentiate the given function. Transcribed Image Text: y 3 x + 5
Answer Preview: 3 x 5 dy x…

, Chapter: 3 -Problem: 81 >> In Exercises 78 through 81, use a graphing utility to sketch the graph of f(x). Then find f'(x) and graph it on the same axes (screen) as f(x). Finally, use TRACE, ZOOM, or the ZERO command to find the values of x where f'(x) = 0.f(x) = (1 ? x1/2)1/2
Answer Preview: We see from the graph that there …

, Chapter: 6 -Problem: 2 >> In each case, either evaluate the given improper integral or show that it diverges. Transcribed Image Text: a. C. +?o 1 Si +00 36 1 dx X (x + 1)² dx b. d. +00 Si -2x xe dx +00 ? -1² xe dx
Answer Preview: a b c d 00 1 5 d…

, Chapter: 4 -Problem: 70 >> In Exercises 69 through 72, the cost C(x) of producing x units of a particular commodity is given. In each case: (a) Find the marginal cost C'(x). (b) Determine the level of production x for which the average cost is minimized. C(x) = 100e0.01x Transcribed Image Text: A(x) = C(x) X
Answer Preview: a b A x 0 when x 100 f…

, Chapter: 3 -Problem: 40 >> In Exercises 39 through 42, the derivative f'(x) of a differentiable function f (x) is given. In each case,(a) Find intervals of increase and decrease for f(x).(b) Determine values of x for which relative maxima and minima occur on the graph of f(x).(c) Find f"(x), and determine intervals of concavity for the graph of f(x).(d) For what values of x do inflection points occur on the graph of f(x)?f'
Answer Preview: a f x x 2 x 1 3 0 when x 0 1 The interva…

, Chapter: 7 -Problem: 9 >> In Exercises 1 through 20, compute all first-order partial derivatives of the given function.f(s, t) = 3t/2s
Answer Preview: f s t fs ft …

, Chapter: 8 -Problem: 45 >> In Exercises 43 through 48, solve the given equation by factoring.x2 + 14x + 49 = 0
Answer Preview: To solve the equation x 2 14x 49 0 by factoring we need to find two binomials whose prod…

, Chapter: 5 -Problem: 59 >> The owner of a fast-food chain determines that if x thousand units of a new meal item are supplied, then the marginal price at that level of supply is given by where p(x) is the price (in dollars) per unit at which all x thousand meal units will be sold. Currently, 5,000 units are being supplied at a price of $2.20 per unit. a. Find the supply (price) function p(x). b. If 10,000 meal units are su
Answer Preview: a When 5 thousand units a…

, Chapter: 5 -Problem: 30 >> In Exercises 21 through 30, evaluate the indicated definite integral. Transcribed Image Text: [² 1 x(ln x)² 2 dx
Answer Preview: 1 Let u lnx Then …

, Chapter: 7 -Problem: 64 >> The difference between an animal’s surface temperature and that of the surrounding air causes a transfer of energy by convection. The coefficient of convection h is given by where V (cm/sec) is wind velocity, D(cm) is the diameter of the animal’s body, and k is a constant. a. Find the partial derivatives hV and hD. Interpret these derivatives as rates. b. Compute the ratio hV/hD.
Answer Preview: a b With h wil …

, Chapter: 3 -Problem: 21 >> In Exercises 13 through 26, determine where the given function is increasing and decreasing, and where its graph is concave up and concave down. Find the relative extrema and inflection points, and sketch the graph of the function.f(s) = 2s(s + 4)3
Answer Preview: The critical value s 4 corresponds to the point 4 0 which is not a relative extremum Ho…

, Chapter: 4 -Problem: 50 >> Suppose an environmental change affects the organism in Exercise 49 in such a way that an individual is only half as likely as before to survive to age x years. If the number of female births f(x) remains the same, how is the ideal age for reproduction affected by this change? Data from Exercises 49Suppose that for a particular semelparous organism, the likelihood of an individual surviving to age
Answer Preview: p x e 0 2x f x 5x 0 9 The per capita rate of repr…

, Chapter: 7 -Problem: 11 >> In Exercises 5 through 12, use the formulas to find the corresponding least-squares line.(?2.1, 3.5), (?1.3, 2.7), (1.5, 1.3), (2.7, ?1.5)
Answer Preview: So the equation of the least squares line is y 0 915x 1 68…

, Chapter: 2 -Problem: 56 >> A toy rocket rises vertically in such a way that t seconds after liftoff, it is h(t) = ?16t2 + 200t feet above ground. a. How high is the rocket after 6 seconds?b. What is the average velocity of the rocket over the first 6 seconds of flight (between t = 0 and t = 6)?c. What is the (instantaneous) velocity of the rocket at liftoff (t = 0)? What is its velocity after 40 seconds?
Answer Preview: a The rocket is h 6 576 1200 624 feet above ground …

, Chapter: 4 -Problem: 9 >> In Exercises 5 through 12, evaluate the given expressions.a. (33)(3?2) b. (42/3)(22/3)
Answer Preview: a b…

, Chapter: 2 -Problem: 10 >> In Exercises 7 through 10, use increments to make the required estimate. Estimate the percentage change in the function as x decreases from 5 to 4.6. Transcribed Image Text: f(x) = 3x + 2 X
Answer Preview: Thus f x will decrease …

, Chapter: 3 -Problem: 50 >> In Exercises 49 through 52, the graph of a function f is given. In each case, sketch a possible graph for f'. Transcribed Image Text: y ??? # 0 12 23 3 4 5 6 X
Answer Preview: 17 4 2 …

, Chapter: 6 -Problem: 8 >> In Exercises 1 through 14, approximate the given integral using  (a) The trapezoidal rule   (b) Simpson’s rule with the specified number of subintervals. Transcribed Image Text: 2 fee Ma dx; n = 10
Answer Preview: a b Simpson…

, Chapter: 3 -Problem: 44 >> Find constants A and B so that the graph of the function will have x = 4 as a vertical asymptote and y = ?1 as a horizontal asymptote. Once you find A and B, sketch the graph of f(x). Transcribed Image Text: f(x) || Ax + 2 8 Bx
Answer Preview: For a vertical asympt…

, Chapter: 7 -Problem: 7 >> Evaluate the double integrals in Exercises 1 through 18. Transcribed Image Text: xp kp & x* JJ
Answer Preview: 4 1 xy …

, Chapter: 8 -Problem: 47 >> In Exercises 29 through 58, factor the given polynomial using integer coefficients.x2 ? 7x ? 18
Answer Preview: To factor the polynomial x 2 7x 18 we need to find two binomials whose prod…

, Chapter: 5 -Problem: 62 >> An environmentalist finds that a certain type of tree grows in such a way that its height h(t) after t years is changing at the rate of If the tree was 2 feet tall when it was planted, how tall will it be in 27 years? Transcribed Image Text: h' (t) = 0.212/3+ Vt ft/yr
Answer Preview: h t 0 21 3 2 h t h t …

, Chapter: 5 -Problem: 21 >> In Exercises 1 through 30, find the indicated integral. Check your answers by differentiation. Transcribed Image Text: fa³-2 3 (1-5) dx - 21²
Answer Preview: I f x 2x 5 dix X x …

, Chapter: 7 -Problem: 56 >> In Exercises 54 through 57, find the partial derivatives fx and fy and then use your graphing utility to determine the critical points of each function.f(x, y) = 6x2 + 12xy + y4 + x ? 16y ? 3
Answer Preview: A graphing utility reveals that y …

, Chapter: 3 -Problem: 25 >> In Exercises 23 through 28, compute the elasticity of demand for the given demand function D(p) and determine whether the demand is elastic, inelastic, or of unit elasticity at the indicated price p.D(p) = 200 ? p2; p = 10
Answer Preview: D p 200 p E p E 10 …

, Chapter: 4 -Problem: 31 >> In Exercises 21 through 36, solve the given equation for x. Transcribed Image Text: In x=(In 16 + 2 In 2) 1370
Answer Preview: 1 Inx ln 16 2 ln …

, Chapter: 5 -Problem: 27 >> In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. Transcribed Image Text: *5 [²12² J2 (2 + 2t + 31²) dt
Answer Preview: 2 2t 31 …

, Chapter: 2 -Problem: 65 >> An object moves along a straight line so that after t minutes, its distance from its starting point is a. At what velocity is the object moving at the end of 4 minutes? b. How far does the object actually travel during the fifth minute? Transcribed Image Text: D(t) 10t + 5 t + 1 - 5 meters.
Answer Preview: a Speed rate o…

, Chapter: 4 -Problem: 11 >> In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many key features as possible (high and low points, points of inflection, vertical and horizontal asymptotes, intercepts, cusps, vertical tangents).f(x) = xex
Answer Preview: When x 2 f x 0 so f is concave up Since the concavity changes at x 2 the point …

, Chapter: 2 -Problem: 8 >> In Exercises 1 through 12, use the chain rule to compute the derivative dy/dx and simplify your answer. Transcribed Image Text: = n 6 – x = Vu 1 || y
Answer Preview: dy dx 1 u …

, Chapter: 3 -Problem: 45 >> In Exercises 43 through 46, the first derivative f'(x) of a certain function f(x) is given. In each case,(a) Find intervals on which f is increasing and decreasing.(b) Find intervals on which the graph of f is concave up and concave down.(c) Find the x coordinates of the relative extrema and inflection points of f.(d) Sketch a possible graph for f(x)f'(x) =  5 ? x2
Answer Preview: a b c At x 5 there is a rel…

, Chapter: 6 -Problem: 13 >> In Exercises 1 through 26, use integration by parts to find the given integral. Transcribed Image Text: X ?x + 2 dx
Answer Preview: both terms are easy to integra…

, Chapter: 3 -Problem: 13 >> In Exercises 13 through 26, determine where the given function is increasing and decreasing, and where its graph is concave up and concave down. Find the relative extrema and inflection points, and sketch the graph of the function. Transcribed Image Text: f(x) = -=-x³- 3 - 9x + 2
Answer Preview: Overall f is increasing for x 3 decreasin…

, Chapter: 7 -Problem: 11 >> In Exercises 1 through 16, use the method of Lagrange multipliers to find the indicated extremum. You may assume the extremum exists.Find the maximum and minimum values of f(x, y) = exy subject to x2 + y2 = 4.
Answer Preview: So the constrained maximum is e 2 and the constrained …

, Chapter: 8 -Problem: 55 >> In Exercises 29 through 58, factor the given polynomial using integer coefficients.x5 + x2
Answer Preview: To factor the polynomial x 5 x 2 we can factor out the greatest common factor w…

, Chapter: 5 -Problem: 49 >> A square cabin with a plot of land adjacent to a lake is shown in the accompanying figure. If a coordinate system is set up as indicated, with distances given in yards, the lakefront boundary of the property is part of the curve y = 10e0.04x. Assuming that the cabin costs $2,000 per square yard and the land in the plot outside the cabin (the shaded region in the figure) costs $800 per square yard,
Answer Preview: Total cost cost of cabin cost of land cost of cabin area o…

, Chapter: 5 -Problem: 24 >> In Exercises 19 through 24, find the average value of the given function f (x) over the specified interval a ? x ? b. Transcribed Image Text: x + 1 x² + 2x + 6 over 1 ? x ? 1
Answer Preview: The average value is 1 x 1 1 1 J …

, Chapter: 7 -Problem: 61 >> The marketing manager for a certain company has compiled these data relating monthly advertising expenditure and monthly sales (both measured in units of $1,000): a. Plot these data on a graph. b. Find the least-squares line, and add it to the graph in part (a). c. Use the least-squares line to predict monthly sales if the monthly advertising expenditure is $5,000.
Answer Preview: a Let x denote the monthly advertising expenditure and y th…

, Chapter: 3 -Problem: 28 >> In Exercises 17 through 32, sketch the graph of the given function. Transcribed Image Text: f(x) = 1 V1-x²
Answer Preview: x 1 and x 1 are ve…

, Chapter: 5 -Problem: 18 >> In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. Transcribed Image Text: ? (5 (5 - 2t) dt
Answer Preview: 5 2…

, Chapter: 2 -Problem: 70 >> a. Show that b. Find dy/dx where y = (2x + 1)(x ? 3)(1 ? 4x). Transcribed Image Text: dh d dx dg -[fgh] = fg7x + fh- +fh+gh- dx dx df dx
Answer Preview: a b d dx fgh fg h …

, Chapter: 4 -Problem: 9 >> In Exercises 1 through 38, differentiate the given function.f(x) = (1 ? 3ex)2
Answer Preview: f x 1 3e …

, Chapter: 2 -Problem: 14 >> In Exercises 14 through 17, find an equation for the tangent line to the graph of the given function at the specified point.f(x) = x2 ? 3x + 2; x = 1
Answer Preview: f 1 0 The slope of the ta…

, Chapter: 3 -Problem: 67 >> Suppose a particular tissue culture has area A(t) at time t and a potential maximum area M. Based on properties of cell division, it is reasonable to assume that the area A grows at a rate jointly proportional to ?A(t) and M ? A(t); that is, where k is a positive constant. a. Let R(t) = A'(t) be the rate of tissue growth. Show that R'(t) = 0 when A(t) = M/3. b. Is the rate of tissue growth greate
Answer Preview: a R t 0 when M 3A t 0 …

, Chapter: 6 -Problem: 7 >> In Exercises 1 through 26, use integration by parts to find the given integral. Transcribed Image Text: Sve ve -v/5 dv
Answer Preview: Both terms are easy to integrate however the d…

, Chapter: 5 -Problem: 36 >> In Exercises 3 through 36, find the indicated integral and check your answer by differentiation. Transcribed Image Text: 2/3 (²-1) ²³. dx
Answer Preview: 1 2 X 1 Let u 1 then du X SG …

, Chapter: 3 -Problem: 14 >> Farmers can get $8 per bushel for their potatoes on July 1, and after that, the price drops by 8 cents per bushel per day. On July 1, a farmer has 80 bushels of potatoes in the field and estimates that the crop is increasing at the rate of 1 bushel per day. When should the farmer harvest the potatoes to maximize revenue?
Answer Preview: Let x be the number of days following July 1 st when the farmer shoul…

, Chapter: 7 -Problem: 1 >> In Exercises 1 through 20, compute all first-order partial derivatives of the given function.f(x, y) = 7x ? 3y + 4
Answer Preview: f x …

, Chapter: 8 -Problem: 68 >> In Exercises 43 through 76, simplify the given expression as much as possible. Assume a, b, and c are positive real numbers. Transcribed Image Text: 5 8? a -16 c² 7 C
Answer Preview: To simplify the given expression let s break it down step by step We have the expressio…

, Chapter: 5 -Problem: 47 >> In Exercises 47 through 50, sketch the Lorenz curve y = L(x) and find the corresponding Gini index.L(x) = x3/2
Answer Preview: GI 2 f x …

, Chapter: 5 -Problem: 27 >> The population density r miles from the center of a certain city is  D(r) = 25,000e?0.05r2 people per square mile. How many people live between 1 and 2 miles from the city center?
Answer Preview: and the limits of integra…

, Chapter: 7 -Problem: 54 >> In Exercises 54 through 57, find the partial derivatives fx and fy and then use your graphing utility to determine the critical points of each function.f(x, y) = (x2 + 3y ? 5)e?x2?2y2
Answer Preview: The critical points are 0 0 138 0 1 …

, Chapter: 3 -Problem: 22 >> In Exercises 21 through 24, find all critical numbers for the given function f(x) and use the second derivative test to determine which (if any) critical points are relative maxima or relative minima.f(x) = x(2x ? 3)2
Answer Preview: f x x 2x 3 f x x 2 2x 3 2 2x 3 2x 3 6x 3 0 …

, Chapter: 5 -Problem: 16 >> In Exercises 3 through 36, find the indicated integral and check your answer by differentiation. Transcribed Image Text: y² (³ + 5)2 dy
Answer Preview: 13 5 Let u y3 5 then du …

, Chapter: 2 -Problem: 75 >> Use a graphing utility to sketch the curve f(x) = x2(x ? 1), and on the same set of coordinate axes, draw the tangent line to the graph of f (x) at x = 1. Use TRACE and ZOOM to find where f'(x) = 0.
Answer Preview: To use a graphing utility to sketch The calculator draws the line tan…

, Chapter: 4 -Problem: 14 >> In Exercises 13 through 20, use logarithmic rules to simplify each expression.log3(x5y?2)
Answer Preview: 2 log3 xy2 log3 x …

, Chapter: 2 -Problem: 13 >> In Exercises 1 through 28, differentiate the given function.y = 9/?t
Answer Preview: 9 9t 1 2 …

, Chapter: 3 -Problem: 63 >> The concentration of a drug t hours after being injected into the arm of a patient is given by Sketch the graph of the concentration function. When does the maximum concentration occur? Transcribed Image Text: C(t) = 0.15t ² +0.81
Answer Preview: Note that since degree of num…

, Chapter: 6 -Problem: 9 >> In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. Transcribed Image Text: 10 +00 5e-2x dx
Answer Preview: N 2x fo 5e x d…

, Chapter: 4 -Problem: 73 >> Instant coffee is made by adding boiling water (212ºF) to coffee mix. If the air temperature is 70ºF, Newton’s law of cooling says that after t minutes, the temperature of the coffee will be given by a function of the form f(t) = 70 + Ae?kt. After cooling for 2 minutes, the coffee is still 15ºF too hot to drink, but 2 minutes later it is just right. What is this “ideal” temperature for drinking?
Answer Preview: Using the quadratic formula Since 72 …

, Chapter: 3 -Problem: 10 >> In Exercises 9 through 22, find the intervals of increase and decrease for the given function.f(t) = t3 + 3t2 + 1
Answer Preview: f t t 3t 1 f t 3t 6t 3t …

, Chapter: 7 -Problem: 3 >> Evaluate the double integrals in Exercises 1 through 18. Transcribed Image Text: In 20 10 -1 2xe dx dy
Answer Preview: 20 21 2xe dx d…

, Chapter: 8 -Problem: 48 >> In Exercises 43 through 48, solve the given equation by factoring. Transcribed Image Text: 4 + || 12 Xx
Answer Preview: To solve the equation 4 9 x 2 12 x by factoring let s rewrite it in a more manag…

, Chapter: 5 -Problem: 49 >> Use integration to show that a right circular cone of height h and top radius r has volume Transcribed Image Text: 1 V v==arth 3
Answer Preview: Volume 7ydx Since the hy…

, Chapter: 5 -Problem: 26 >> In Exercises 21 through 30, evaluate the indicated definite integral. Transcribed Image Text: [ (3x + 6) 1(x + 4x + 5)? dx
Answer Preview: Let u x 4x 5 Then du 2x 4 d…

, Chapter: 7 -Problem: 57 >> Find three positive numbers x, y, and z so that x + y + z = 20 and the product P = xyz is a maximum.
Answer Preview: The sum of the three numbers is x y z 20 so z 20 x y Their product is Since t…

, Chapter: 3 -Problem: 4 >> Determine all vertical and horizontal asymptotes for the graph of each of these functions. Transcribed Image Text: a. f(x) b. f(x) c. f(x) d. f(x) = 2x - 1 x + 3 X 2²-1 + x - 1 2x² + x3 1 X 1 ?x
Answer Preview: a b c so there are vertical asymptotes o…

, Chapter: 5 -Problem: 31 >> Environmentalists estimate that the population of a certain endangered species is currently 3,000. The population is expected to be growing at the rate of R(t) = 10e0.01t individuals per year t years from now, and the fraction that survive t years is given by S(t) = e?0.07t. What will the population of the species be in 10 years?
Answer Preview: P 10 3 000e 0 07 10 10 10 e0 …

, Chapter: 2 -Problem: 63 >> In Exercises 61 through 64, the position s(t) of an object moving along a straight line is given. In each case:(a) Find the object’s velocity v(t) and acceleration a(t).(b) Find all times t when the acceleration is 0.s(t) = ?t3 + 7t2 + t + 2
Answer Preview: s t t 3 …

, Chapter: 4 -Problem: 16 >> In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many key features as possible (high and low points, points of inflection, vertical and horizontal asymptotes, intercepts, cusps, vertical tangents).f(x) = ex + e?x
Answer Preview: 0 2 is the absolute minimu…

, Chapter: 2 -Problem: 12 >> In Exercises 1 through 18, differentiate the given function. Transcribed Image Text: y 2+1 1-2
Answer Preview: z z 1 4t …

, Chapter: 3 -Problem: 50 >> After a presidential election, the proportion h(p) of seats in the House of Representatives won by the party of the winning presidential candidate may be modeled by the cube rule where p is the proportion of the popular vote received by the winning presidential candidate. a. Find h'(p) and h"(p). b. Sketch the graph of h(p). c. In 1964, the Democrat Lyndon Johnson received 61% of the popular vote
Answer Preview: a b c The cube rule predicts that 79 of …

, Chapter: 6 -Problem: 4 >> In Exercises 1 through 10, use integration by parts to find the given integral. Transcribed Image Text: -9 y dy V4 - 5y
Answer Preview: u y du dy y 9 4 5y dv V d…

, Chapter: 5 -Problem: 42 >> In Exercises 35 through 42, the slope f(x) at each point (x, y) on a curve y = f(x) is given along with a particular point (a, b) on the curve. Use this information to find f(x). Transcribed Image Text: f'(x) = 3 X 4; (1, 0)
Answer Preview: f x f x dx 3 …

, Chapter: 3 -Problem: 36 >> In Exercises 35 through 44, use calculus to sketch the graph of the given function.f(x) = 3x4 ? 4x3
Answer Preview: 0 0 is neither a …

, Chapter: 7 -Problem: 4 >> In Exercises 1 through 10, find the partial derivatives fx and fy.f(x, y) = xe?y + ye?x
Answer Preview: X f x y …

, Chapter: 8 -Problem: 47 >> In Exercises 43 through 48, solve the given equation by factoring. Transcribed Image Text: 1 1 X | 2 = 0
Answer Preview: To solve the equation 1 1 x 2 x 2 0 by factoring we can first rewrite the equation in a commo…

, Chapter: 5 -Problem: 53 >> The marginal revenue from the sale of x units of a particular commodity is estimated to be where R(x) is revenue in dollars. a. Find R(x), assuming that R(0) = 0. b. What revenue should be expected from the sale of 1,000 units? Transcribed Image Text: R'(x) = 50+ 3.5xe-0.01x² dollars per unit
Answer Preview: a b R x R x dx f 50 3 5xe 0 01x dx 50f dx 3 …

, Chapter: 5 -Problem: 29 >> In Exercises 29 through 34, find the Gini index for the given Lorenz curve.L(x) = x3
Answer Preview: GI…

, Chapter: 7 -Problem: 53 >> In manufacturing semiconductors, it is necessary to use water with an extremely low mineral content, and to separate water from contaminants, it is common practice to use a membrane process called reverse osmosis. A key to the effectiveness of such a process is the osmotic pressure, which may be determined by the van’t Hoff equation:* P(N, C, T) = 0.075NC(273.15 + T) where P is the osmotic pressur
Answer Preview: P 2 0 53 2…

, Chapter: 3 -Problem: 21 >> In Exercises 17 through 22, you are given the price p(q) at which q units of a particular commodity can be sold and the total cost C(q) of producing the q units. In each case:(a) Find the revenue function R(q), the profit function P(q), the marginal revenue R'(q), and marginal cost C'(q). Sketch the graphs of P(q), R'(q), and C'(q) on the same coordinate axes and determine the level of production
Answer Preview: a The profit function is Use the maximum function …

, Chapter: 5 -Problem: 15 >> In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. Transcribed Image Text: 2 15 -1 5 dx
Answer Preview: 5dx…

, Chapter: 2 -Problem: 67 >> Use a graphing utility to graph the curve Find the equation of each horizontal tangent to the curve. (The curve is called a cardioid.) Transcribed Image Text: x² + y² = ???x² + y² + x.
Answer Preview: To use the graphing utility to graph curve it …

, Chapter: 4 -Problem: 38 >> If log10 x = ?3, what is ln x?
Answer Preview: log10 x …

, Chapter: 7 -Problem: 38 >> In Exercises 37 and 38, you will need to know that a closed cylinder of radius R and length L has volume V = ?R2L and surface area S = 2?RL + 2?R2. The volume of a hemisphere of radius R is V = 2/3?R3 and its surface area is S = 2?R2. A bacterium is shaped like a cylindrical rod with two hemispherical “caps” on the ends. If the volume of the bacterium is fixed, what must be true about its radius R
Answer Preview: The constraint is the volume of the two hemis…

, Chapter: 2 -Problem: 18 >> At a certain factory, the daily output is Q(L) = 60,000L1/3 units, where L denotes the size of the labor force measured in worker-hours. Currently 1,000 worker-hours of labor are used each day. Estimate the effect on output that will be produced if the labor force is cut to 940 worker-hours.
Answer Preview: The approximate effect on outpu…

, Chapter: 3 -Problem: 47 >> In Exercises 45 through 48, the derivative of a function f(x) is given. In each case, find the critical numbers of f(x) and classify each as corresponding to a relative maximum, a relative minimum, or neither. Transcribed Image Text: f'(x) (x + 1)²(4-3x)³ (x² + 1)²
Answer Preview: When x 1 f does not have a rela…

, Chapter: 6 -Problem: 17 >> In Exercises 11 through 18, either find a number k such that the given function is a probability density function or explain why no such number exists. Transcribed Image Text: f(x) = xe 0 -kx for x ? 0 otherwise
Answer Preview: Setting this equal to one k 1 Then for x 0 f x …

, Chapter: 5 -Problem: 32 >> The population of a small town is currently 85,000. A study commissioned by the mayor’s office finds that people are settling in the town at the rate of R(t) = 1,200e0.01t per year and that the fraction of the population who continue to live in the town t years after arriving is given by S(t) = e?0.02t. How many people will live in the town in 10 years?
Answer Preview: This is a survival and renewal problem with or approx…

, Chapter: 3 -Problem: 14 >> In Exercises 1 through 16, find the absolute maximum and absolute minimum (if any) of the given function on the specified interval. Transcribed Image Text: f(x) = 1 it > 0
Answer Preview: There is no absolute maximu…

, Chapter: 7 -Problem: 9 >> In Exercises 1 through 10, find the partial derivatives fx and fy. Transcribed Image Text: f(x, y) = x2² - y² 2x + y
Answer Preview: f x y fx fy zA zx 2x …

, Chapter: 8 -Problem: 64 >> In Exercises 59 through 74, solve the given equation by factoring.x2 ? 25 = 0
Answer Preview: To solve the equation x 2 25 0 by factoring we can use the difference of squar…

, Chapter: 5 -Problem: 52 >> Suppose it has been determined that the marginal revenue associated with the production of x units of a particular commodity is R'(x) = 240 ? 4x dollars per unit. What is the revenue function R(x)? You may assume R(0) = 0. What price will be paid for each unit when the level of production is x = 5 units?
Answer Preview: where p is the price per un…

, Chapter: 5 -Problem: 24 >> In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. Transcribed Image Text: L ( 1 - - 1 - ) d x dx e
Answer Preview: 1 Le 1 et e …

, Chapter: 7 -Problem: 40 >> Suppose the utility derived by a consumer from x units of one commodity and y units of a second commodity is given by the utility function U(x, y) = 2x3y2. The consumer currently owns x = 5 units of the first commodity and y = 4 units of the second. Find the consumer’s current level of utility, and sketch the corresponding indifference curve.
Answer Preview: The utility yields an indi…

, Chapter: 3 -Problem: 32 >> A manufacturer estimates that if x units of a particular commodity are produced, the total cost will be C(x) dollars, where  C(x) = x3 ? 24x2 + 350x + 338 a. At what level of production will the marginal cost C'(x) be minimized? b. At what level of production will the average cost be minimized? Transcribed Image Text:
Answer Preview: a This leads to a relative minimum as …

, Chapter: 5 -Problem: 10 >> In Exercises 1 through 20, find the indicated indefinite integral. Transcribed Image Text: [(3. (3x + 1)?3x² + 2x + 5 dx
Answer Preview: Let u 3x 2x 5 Then du …

, Chapter: 2 -Problem: 68 >> According to Debye’s formula in physical chemistry, the orientation polarization P of a gas satisfies where ?, k, and N are positive constants, and T is the temperature of the gas. Find the rate of change of P with respect to T. Transcribed Image Text: 4 P = = N 3 TN ?² 3??
Answer Preview: 4 P IN …

, Chapter: 4 -Problem: 40 >> If log3(x ? 5) = 2, what is ln x?
Answer Preview: log3 x 5 …

, Chapter: 2 -Problem: 8 >> In Exercises 1 through 18, differentiate the given function. Transcribed Image Text: y || 2x - 3 5x+4
Answer Preview: y dy dx 2x 3 5x …

, Chapter: 6 -Problem: 15 >> In Exercises 1 through 26, use integration by parts to find the given integral. Transcribed Image Text: Livets dx + 5
Answer Preview: both terms are easy to integra…

, Chapter: 4 -Problem: 72 >> According to Fick’s law* f(t) = C(1 ? e?kt), where f(t) is the concentration of solute inside a cell at time t, C is the (constant) concentration of solute surrounding the cell, and k is a positive constant. Suppose that for a particular cell, the concentration on the inside of the cell after 2 hours is 0.8% of the concentration outside the cell.a. What is k?b. What is the percentage rate of chang
Answer Preview: a b f t C …

, Chapter: 3 -Problem: 42 >> In Exercises 39 through 42, the second derivative f"(x) of a function is given. In each case, use this information to determine where the graph of f(x) is concave upward and concave downward and find all values of x for which an inflection point occurs. Transcribed Image Text: f"(x) || x² + x = 2 x
Answer Preview: x 2 and x 1 are the x coord…

, Chapter: 7 -Problem: 4 >> In Exercises 1 through 20, compute all first-order partial derivatives of the given function.f(x, y) = 2x( y ? 3x) ? 4y
Answer Preview: f x y 2x y…

, Chapter: 8 -Problem: 69 >> In Exercises 43 through 76, simplify the given expression as much as possible. Assume a, b, and c are positive real numbers.(a4b2c12)?1/2
Answer Preview: To simplify the expression a 4b 2c 12 1 2 we can apply the ru…

, Chapter: 5 -Problem: 49 >> A manufacturer estimates marginal revenue to be R'(q) = 100q?1/2 dollars per unit when the level of production is q units. The corresponding marginal cost has been found to be 0.4q dollars per unit. Suppose the manufacturer’s profit is $520 when the level of production is 16 units. What is the manufacturer’s profit when the level of production is 25 units?
Answer Preview: Now profit revenues costs so R q …

, Chapter: 5 -Problem: 21 >> In Exercises 21 through 30, evaluate the indicated definite integral. Transcribed Image Text: Some (5x4 - 8x³ + 1) dx
Answer Preview: 5x4 8…

, Chapter: 7 -Problem: 60 >> In Exercises 58 through 61, use the method of Lagrange multipliers to find the indicated maximum or minimum. You will need to use the graphing utility or the solve application on your calculator. Minimize subject to x + 2y = 7. Transcribed Image Text: f(x,y) 3 1 + 2 ??
Answer Preview: Solving reveals the points 41 80 17 40 2 77 4 88 and 2 96 2 02 f …

, Chapter: 3 -Problem: 20 >> In Exercises 17 through 32, sketch the graph of the given function.f(x) = 3x4 ? 4x2 + 3
Answer Preview: 0 3 is a relat…

, Chapter: 5 -Problem: 14 >> In Exercises 5 through 18, sketch the given region R and then find its area.R is the triangle bounded by the line y = 4 ? 3x and the coordinate axes.
Answer Preview: 0 4 0 2 3 2 1 4 3 …

, Chapter: 2 -Problem: 77 >> Let f(x) = (3x + 5)(2x3 ? 5x + 4). Use a graphing utility to graph f (x) and f'(x) on the same set of coordinate axes. Use TRACE and ZOOM to find where f'(x) = 0.
Answer Preview: Use trace and zoom in to find the x intercepts of f x or use the zero …

, Chapter: 4 -Problem: 39 >> If log5(2x) = 7, what is ln x?
Answer Preview: log5 2x 7 Rewritin…

, Chapter: 2 -Problem: 9 >> In Exercises 3 through 13, find the derivative of the given function. Transcribed Image Text: y = ( x x+ X 2 5 V3x
Answer Preview: y x x x dy X d…

, Chapter: 6 -Problem: 17 >> In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. Transcribed Image Text: ?? ??- 2xe JO ?0+.
Answer Preview: 3x for 2 xe x dx lim 2f N N Use integration by parts wi…

, Chapter: 5 -Problem: 42 >> A marketing survey indicates that t months after a new type of computerized air purifier is introduced to the market, sales will be generating profit at the rate of P'(t) thousand dollars per month, where a. When is the rate of profitability positive and when is it negative? When is the rate increasing and when is it decreasing? b. At what time t = tm is monthly profit maximized? Find the net cha
Answer Preview: a Since t 0 the sign of P t is determined by the sign of 1 4In 0 5t 1 which will b…

, Chapter: 3 -Problem: 8 >> In Exercises 1 through 10, determine intervals of increase and decrease and intervals of concavity for the given function. Then sketch the graph of the function. Be sure to show all key features such as intercepts, asymptotes, high and low points, points of inflection, cusps, and vertical tangents.G(x) = (2x ? 1)2(x ? 3)3
Answer Preview: is a relative maximum 1 5 …

, Chapter: 6 -Problem: 60 >> A new virus has just been declared an epidemic by health officials. Currently, 10,000 people have the disease and it is estimated that t days from now new cases will be reported at the rate of R(t) = 10te?0.1t people per day. If the fraction of victims who still have the virus t days after first contracting it is given by S(t) = e?0.015t, how many people will be infected by the virus 90 days from
Answer Preview: The number of cases in T days is given by the surviva…

, Chapter: 8 -Problem: 75 >> In Exercises 75 through 82, solve the given quadratic equation by completing the square.x2 + 2x ? 3 = 0
Answer Preview: To solve the quadratic equation x 2 2x 3 0 by completing the squa…

, Chapter: 5 -Problem: 57 >> A certain oil well that yields 400 barrels of crude oil per month will run dry in 2 years. The price of crude oil is currently $98 per barrel and is expected to rise at the constant rate of 40 cents per barrel per month. If the oil is sold as soon as it is extracted from the ground, how much total revenue will be obtained from the well?
Answer Preview: Rate total revenue changes barrels …

, Chapter: 5 -Problem: 34 >> Repeat Exercise 33 for C(q) = 2q3 ? 59q2 + 4q + 7,600 and p = 124 ? 2q. Data from Exercises 33A manufacturer of machinery parts determines that q units of a particular piece will be sold when the price is p = 110 ? q dollars per unit. The total cost of producing those q units is C(q) dollars, wherea. How much profit is derived from the sale of the q units at p dollars per unit?b. For what value of
Answer Preview: a The dollar price per unit is P 124 2q …

, Chapter: 7 -Problem: 36 >> In Exercises 35 through 40, use the chain rule to find dz/dt. Express your answer in terms of x, y, and t.z = x2y; x = 3t + 1, y = t2 ? 1
Answer Preview: z xy x 3t 1 y …

, Chapter: 3 -Problem: 25 >> A plastics firm has received an order from the city recreation department to manufacture 8,000 special Styrofoam kickboards for its summer swimming program. The firm owns 10 machines, each of which can produce 30 kickboards an hour. The cost of setting up the machines to produce the kickboards is $20 per machine. Once the machines have been set up, the operation is fully automated and can be overs
Answer Preview: a Let x denote the number of machines used and C x the corr…

, Chapter: 5 -Problem: 15 >> In Exercises 1 through 30, find the indicated integral. Check your answers by differentiation. Transcribed Image Text: J(² + xVx) dx 2
Answer Preview: I et 2 et e …

, Chapter: 2 -Problem: 58 >> The gross domestic product of a certain country is growing at a constant rate. In 2000 the GDP was 125 billion dollars, and in 2008 it was 155 billion dollars. If this trend continues, at what percentage rate will the GDP be growing in 2015?
Answer Preview: Let G t be the GDP in billions of dollars where t is years an…

, Chapter: 4 -Problem: 10 >> In Exercises 1 through 38, differentiate the given function. Transcribed Image Text: f(x) = V1 + et
Answer Preview: f x 1 ex 1 2 1 F x 1 e …

, Chapter: 2 -Problem: 79 >> The curve y2(2 ? x) = x3 is called a cissoid.a. Use a graphing utility to sketch the curve.b. Find an equation for the tangent line to the curve at all points where x = 1.c. What happens to the curve as x approaches 2 from the left?d. Does the curve have a tangent line at the origin? If so, what is its equation?
Answer Preview: Given y 2 2 x x 3 a The equation does not change as y is replaced by y So the equation is symmet…

, Chapter: 6 -Problem: 8 >> In Exercises 1 through 26, use integration by parts to find the given integral. Transcribed Image Text: we0.1w dw ve
Answer Preview: 1 we 1w dw dv e …

, Chapter: 4 -Problem: 72 >> In Exercises 69 through 72, the cost C(x) of producing x units of a particular commodity is given. In each case: (a) Find the marginal cost C'(x). (b) Determine the level of production x for which the average cost is minimized. C(x) = x2 + 10xe?x Transcribed Image Text: A(x) = C(x) X
Answer Preview: a b For 0 x ln 10 A …

, Chapter: 3 -Problem: 10 >> In Exercises 1 through 16, find the absolute maximum and absolute minimum (if any) of the given function on the specified interval. Transcribed Image Text: g(x) || 1 -9 ;0?x?2
Answer Preview: when x 0 The absolut…

, Chapter: 7 -Problem: 9 >> In Exercises 1 through 16, use the method of Lagrange multipliers to find the indicated extremum. You may assume the extremum exists.Let f(x, y) = 2x2 + 4y2 ? 3xy ? 2x ? 23y + 3. Find the minimum value of the function f(x, y) subject to the constraint x + y = 15.
Answer Preview: g x g y 1 The three Lagrange equations are T…

, Chapter: 8 -Problem: 74 >> In Exercises 43 through 76, simplify the given expression as much as possible. Assume a, b, and c are positive real numbers.(a2/3 + b2/3)(a2/3 ? b2/3)
Answer Preview: To simplify the expression a 2 3 b 2 3 a 2 3 b 2 3 we can use the differ…

, Chapter: 5 -Problem: 47 >> In Exercises 45 through 50, f(x) and g(x) are functions that are continuous on the interval ?3 ? x ? 2 and satisfy In each case, use this information along with rules for definite integrals to evaluate the indicated integral. Transcribed Image Text: [Fox) dx = 5 [²80x) dx = -2 [700 dx = 0 [?8x) f(
Answer Preview: g x dx G 4 …

, Chapter: 5 -Problem: 26 >> In Exercises 15 through 44, evaluate the given definite integral using the fundamental theorem of calculus. Transcribed Image Text: L? (-3.6² (-3x³ 3x² + 2x + 5) dx
Answer Preview: 1 3x 3 …

, Chapter: 7 -Problem: 56 >> The level curves in the land areas of the accompanying figure indicate ice elevations above sea level (in meters) during the last major ice age (approximately 18,000 years ago). The level curves in the sea areas indicate sea surface temperature. For instance, the ice was 1,000 meters thick above New York City, and the sea temperature near the Hawaiian Islands was about 24 ºC. Where on earth was th
Answer Preview: The ice pack was thicke…

, Chapter: 3 -Problem: 27 >> In Exercises 27 through 38, use the second derivative test to find the relative maxima and minima of the given function.f(x) = x3 + 3x2 + 1
Answer Preview: So 0 1 is a relative minimum and …

, Chapter: 5 -Problem: 17 >> In Exercises 1 through 30, find the indicated integral. Check your answers by differentiation. Transcribed Image Text: [u' (3-1) du 3u
Answer Preview: 1 m 1 1 du 3u 1 3 U …

, Chapter: 2 -Problem: 67 >> If an object is dropped or thrown vertically, its height (in feet) after t seconds is H(t) = ?16t2 + V0t + H0, where V0 is the initial speed of the object and H0 is its initial height.a. Derive an expression for the acceleration of the object.b. How does the acceleration vary with time?c. What is the significance of the fact that the answer to part (a) is negative?
Answer Preview: a H t 32t v 0 and the acceleration is H t 32 b Since …

, Chapter: 4 -Problem: 11 >> In Exercises 9 through 12, use logarithmic rules to rewrite each expression in terms of log3 2 and log3 5.log3 100
Answer Preview: log3 100 log3 …

, Chapter: 2 -Problem: 13 >> In Exercises 9 through 22, find dy/dx by implicit differentiation.y2 + 2xy2 ? 3x + 1 = 0
Answer Preview: y 2x 3x 1 0 1 2 …

, Chapter: 6 -Problem: 21 >> In Exercises 21 through 34, either evaluate the given improper integral or show that it diverges. Transcribed Image Text: +00 1 1 + 2x dx
Answer Preview: 00 So dx 1 31 2x Using substi…

, Chapter: 5 -Problem: 37 >> In Exercises 37 through 42, solve the given initial value problem for y = f(x).dy/dx = (3 ? 2x)2 where y = 0 when x = 0
Answer Preview: y dx 3 2x dx dx Let u 32x Then 1 …

, Chapter: 3 -Problem: 11 >> In Exercises 11 and 12, one of the two curves shown is the graph of a certain function f(x) and the other is the graph of its derivative f'(x). Determine which curve is the graph of the derivative, and give reasons for your decision. Transcribed Image Text: 3 O (a) -X f X (b)
Answer Preview: Graph b is the graph of f and graph a is …

, Chapter: 7 -Problem: 2 >> In Exercises 1 through 16, use the method of Lagrange multipliers to find the indicated extremum. You may assume the extremum exists.Find the maximum and minimum values of the function f(x, y) = xy subject to the constraint x2 + y2 = 1.
Answer Preview: f x y xy g x y x y 1 fx y fy x gx 2x 8y 2y so y …

, Chapter: 8 -Problem: 75 >> In Exercises 43 through 76, simplify the given expression as much as possible. Assume a, b, and c are positive real numbers. Transcribed Image Text:

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7 Reviews for Calculus For Business, Economics And The Social And Life Sciences Textbook Questions And Answers