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Chapter: 13 -Problem: 28 >> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions.f (x) + h(x)
Answer Preview: f x h x 2 2 …

, Chapter: 10 -Problem: 9 >> Find a constant solution of y? = t2y - 5t2.
Answer Preview: y t 2 y 5t 2 t …

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, Chapter: 3 -Problem: 42 >> The graph of x3 + y3 = 9xy is the folium of Descartes shown in Fig. 4.(a) Find dy/dx by implicit differentiation.(b) Find the slope of the curve at (2, 4). Transcribed Image Text: x + y + 1 = 0 Asymptote y -X x² + y² = 9xy Figure 4 Folium of Descartes.
Answer Preview: x 3 y 3 9xy a b 3 …

, Chapter: 8 -Problem: 2 >> Convert the following to radian measure.18°, 72°, 150°
Answer Preview: 180 180 18 18 72 7…

, Chapter: 2 -Problem: 18 >> A canvas wind shelter for the beach has a back, two square sides, and a top. Find the dimensions for which the volume will be 250 cubic feet and that requires the least possible amount of canvas.
Answer Preview: Let C cost of materials Constraint x 2 …

, Chapter: 9 -Problem: 53 >> Determine ?2x(x2 + 5)dx by making a substitution. Then, determine the integral by multiplying out the integrand and antidifferentiating. Account for the difference in the two results.
Answer Preview: The two methods differ by a cons…

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, Chapter: 2 -Problem: 33 >> Sketch the graph of a function having the given properties.Defined for 0 ? x ? 10; relative maximum point at x = 3; absolute maximum value at x = 10
Answer Preview: y…

, Chapter: 11 -Problem: 15 >> Find the Taylor series at x = 0 of the given function. Use suitable operations (differentiation, substitution, etc.) on the Taylor series at x = 0 ofln(1 + x) Transcribed Image Text: 1 1- x 9 et, or cos x.
Answer Preview: x dx 1 x x x x dx C …

, Chapter: 13 -Problem: 9 >> Express f (x) + g(x) as a rational function. Carry out all multiplications. Transcribed Image Text: f(x) = X x - 8' g(x) = -X x - 4
Answer Preview: X X x x 4 …

, Chapter: 13 -Problem: 33 >> Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(?x - 1). Determine the following functions.g(h(x))
Answer Preview: 1 x 2 x …

, Chapter: 6 -Problem: 11 >> Set-up the definite integral that gives the area of the shaded region. Do not evaluate the integral. Transcribed Image Text: y y = x + // 1 3 y = x - X
Answer Preview: S …

, Chapter: 10 -Problem: 8 >> One or more initial conditions are given for each differential equation in the following exercises. Use the qualitative theory of autonomous differential equations to sketch the graphs of the corresponding solutions. Include a yz-graph if one is not already provided. Always indicate the constant solutions on the ty-graph whether they are mentioned or not.
Answer Preview: 6 3…

, Chapter: 4 -Problem: 52 >> Find k such that 2-x/5 = ekx for all x.
Answer Preview: 2 x 5 2 1 5 115 3 …

, Chapter: 3 -Problem: 42 >> In Exercises, a function h(x) is defined in terms of a differentiable f(x). Find an expression for h?(x).h(x) = (x2 + 2x - 1) f(x)
Answer Preview: h x x 2x …

, Chapter: 6 -Problem: 19 >> Calculate the following integrals. Transcribed Image Text: 4 -| 1 X dx
Answer Preview: 3 1…

, Chapter: 2 -Problem: 47 >> Draw the graph of f (x) = 1/6x3 - x2 + 3x + 3 in the window [-2, 6] by [-10, 20]. It has an inflection point when x = 2, but no relative extreme points. Enlarge the window a few times to convince yourself that there are no relative extreme points anywhere. What does this tell you about f?(x)?
Answer Preview: Since f x is always …

, Chapter: 10 -Problem: 5 >> Twenty years ahead of her retirement, Kelly opened a savings account that earns 5% interest rate compounded continuously, and she contributed to this account at the annual rate of $1200 per year for 20 years. Ten years ahead of his retirement, John opened a similar savings account that earns 5% interest rate compounded continuously and decided to double the annual rate of contribution to $2400 per
Answer Preview: Both accounts satisfy the differential equation y 0 05y …

, Chapter: 10 -Problem: 26 >> On the slope field in Fig. 4(a) or a copy of it, draw an approximation of a portion of the solution curve of the differential equation y? = t - y that goes through the point (0, 2). In your opinion, based on the slope field, can this solution pass through the point (.5, 2.2)?
Answer Preview: This solution w…

, Chapter: 2 -Problem: 31 >> Find the point on the line y = -2x + 5 that is closest to the origin. Transcribed Image Text: City A 6 miles Figure 18 Road Road 11 miles City B 11-a 4 miles
Answer Preview: The distance has its smallest value …

, Chapter: 13 -Problem: 4 >> Draw the following intervals on the number line. Transcribed Image Text: [1, 2]
Answer Preview: 0…

, Chapter: 13 -Problem: 31 >> If f (x) = x2, find f (x + h) - f (x) and simplify.
Answer Preview: x h …

, Chapter: 6 -Problem: 1 >> Write a definite integral or sum of definite integrals that gives the area of the shaded portions in Fig. 21. Transcribed Image Text: 2 0 y -1 Figure 21 1 y = f(x) 2 3 4 X
Answer Preview: A x …

, Chapter: 2 -Problem: 14 >> Refer to Exercise 13. If the cost of the fencing for the boundary is $5 per meter and the dividing fence costs $2 per meter, find the dimensions of the corral that minimize the cost of the fencing. Exercise 13A rectangular corral of 54 square meters is to be fenced off and then divided by a fence into two sections, as shown in Fig. 7(b). Find the dimensions of the corral so that the amount of fenc
Answer Preview: The objective is C 2 …

, Chapter: 10 -Problem: 28 >> One or more initial conditions are given for each differential equation in the following exercises. Use the qualitative theory of autonomous differential equations to sketch the graphs of the corresponding solutions. Include a yz-graph if one is not already provided. Always indicate the constant solutions on the ty-graph whether they are mentioned or not.y? = y - 1/4y2, y(0) = -1, y(0) = 1
Answer Preview: Z 21 1 …

, Chapter: 3 -Problem: 41 >> The graph of x2/3 + y2/3 = 8 is the astroid in Fig. 3.(a) Find dy/dx by implicit differentiation.(b) Find the slope of the tangent line at (8, -8). Transcribed Image Text: y Figure 3 Astroid. 22/3 + y2/3 = 8 X
Answer Preview: x 2 3 y 2 3 8 …

, Chapter: 6 -Problem: 19 >> Combine the integrals into one integral, then evaluate the integral. Transcribed Image Text: 2 ² ??² (³x + 1² x ² ? x ³ ) dx + 3 ? ?² (x² - 2 3x - (x² - 2x + 7)dx
Answer Preview: dx 25 x x x dx x 2x 7 dx 6…

, Chapter: 2 -Problem: 20 >> Properties of various functions are described next. In each case, draw some conclusion about the graph of the function. Transcribed Image Text: H(0) = 0, H'(0) = 0, H"(0) = 1
Answer Preview: 0 0 is …

, Chapter: 10 -Problem: 1 >> Refer to Example 1.(a) How fast was the amount in the account growing when it reached $30,000?(b) How much money was in the account when it was growing at twice the rate of your annual contribution?(c) How long do you have to wait for the money in the account to reach $40,000? Example 1.You invest in a retirement account that pays 6% interest per year. You make an initial deposit of $1000 and plan
Answer Preview: a b c About 11 years and …

, Chapter: 10 -Problem: 36 >> Some homeowner’s insurance policies include automatic inflation coverage based on the U.S. Commerce Department’s construction cost index (CCI). Each year, the property insurance coverage is increased by an amount based on the change in the CCI. Let f (t) be the CCI at time t years since January 1, 1990, and let f (0) = 100. Suppose that the construction cost index is rising at a rate proportional
Answer Preview: y ky k 0 y 0 100 y 2 115 dy 1 dt y k Assuming y 0 dy k …

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, Chapter: 13 -Problem: 1 >> Let f (x) = x2 + 1, g(x) = 9x, and h(x) = 5 - 2x2. Calculate the following functions.f (x) + g(x)
Answer Preview: f x …

, Chapter: 13 -Problem: 29 >> Use the laws of exponents to compute the numbers.51/3 · 2001/3
Answer Preview: 5 1 3…

, Chapter: 6 -Problem: 5 >> Determine the average value of f (x) over the interval from x = a to x = b, wheref (x) = 1/x; a = 1/3, b = 3.
Answer Preview: 1 3 1 1 3 x 3 …

, Chapter: 10 -Problem: 12 >> What is the logistic differential equation?
Answer Preview: The logistic diff…

, Chapter: 4 -Problem: 46 >> Solve the following equations for t.ln( ln 3t) = 0
Answer Preview: In In 3t I…

, Chapter: 10 -Problem: 35 >> One or more initial conditions are given for each differential equation in the following exercises. Use the qualitative theory of autonomous differential equations to sketch the graphs of the corresponding solutions. Include a yz-graph if one is not already provided. Always indicate the constant solutions on the ty-graph whether they are mentioned or not.y? = ky - A, where k and A are positive con
Answer Preview: N z …

, Chapter: 3 -Problem: 38 >> Compute dy/dx using the chain rule in formula (1). State your answer in terms of x only. Transcribed Image Text: y = Vu+1, u = 2x²
Answer Preview: y u 1 u 2x d…

, Chapter: 6 -Problem: 29 >> Find the area in Fig. 27 of the region bounded by y = 1/x2, y = x, and y = 8x, for x ? 0. Transcribed Image Text: y Figure 27 y = 8x y y = x X
Answer Preview: Y y 8x Y y X X X 1 1 2 X First solve 8x This has …

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, Chapter: 9 -Problem: 45 >> Determine the following integrals by making an appropriate substitution. Transcribed Image Text: cos Vx Vx dx
Answer Preview: cos x dx Let u x …

, Chapter: 11 -Problem: 1 >> Determine the sums of the following geometric series when they are convergent. Transcribed Image Text: 1 + 1 6 + 1 + 6² 1 1 64 63 +
Answer Preview: 1 The series …

, Chapter: 2 -Problem: 30 >> Sketch the following parabolas. Include their x- and y-intercepts.y = -x2 + 8x - 13
Answer Preview: y x 8x 13 y 2x 8 y 2 y 0 if x 4 If x 4 y 3 …

, Chapter: 13 -Problem: 14 >> LetandExpress the following as rational functions.f (t) - h(t) Transcribed Image Text: f(x) = X x-2' g(x)= 5-x 5 + x'
Answer Preview: t t 2 t 1 …

, Chapter: 1 -Problem: 33 >> In Exercises, determine the value of a that makes the  function f(x) continuous at x = 0. Transcribed Image Text: for x ? 0 x) = { x + a forx < 0 f(x)
Answer Preview: For the function …

, Chapter: 13 -Problem: 40 >> The revenue R(x) (in thousands of dollars) that a company receives from the sale of x thousand units is given by R(x) = 5x - x2. The sales level x is in turn a function f (d) of the number d of dollars spent on advertising, whereExpress the revenue as a function of the amount spent on advertising. Transcribed Image Text:
Answer Preview: R x 5x x f d 61 R …

, Chapter: 6 -Problem: 3 >> Find all antiderivatives of each following function:f(x) = e3x
Answer Preview: f x e…

, Chapter: 10 -Problem: 10 >> One or more initial conditions are given for each differential equation in the following exercises. Use the qualitative theory of autonomous differential equations to sketch the graphs of the corresponding solutions. Include a yz-graph if one is not already provided. Always indicate the constant solutions on the ty-graph whether they are mentioned or not.y? = 6 - y2, y(0) = -3, y(0) = 3. (See Fig.
Answer Preview: Y …

, Chapter: 3 -Problem: 69 >> The relationship between the area of the pupil of the eye and the intensity of light was analyzed by B. H. Crawford. Crawford concluded that the area of the pupil issquare millimeters when x units of light are entering the eye per unit time.(a) Graph f(x) and f?(x) in the window [0, 6] by [-5, 20].(b) How large is the pupil when 3 units of light are entering the eye per unit time?(c) For what ligh
Answer Preview: a b f 3 10 8 square millimeters …

, Chapter: 3 -Problem: 34 >> Compute d/dx f(g (x)), where f(x) and g(x) are the following: Transcribed Image Text: f(x) 4 ·+ x², g(x) = 1 - x4 X
Answer Preview: 4 f x x g x 1 x4 …

, Chapter: 6 -Problem: 17 >> Draw the region whose area is given by the definite integral. Transcribed Image Text: ?² (8- (8 - 2x)dx
Answer Preview: 8 Y…

, Chapter: 2 -Problem: 15 >> Outline the procedure for solving an optimization problem.
Answer Preview: 1 Draw a picture if possible 2 Decide what quantity Q is to be maxi…

, Chapter: 9 -Problem: 47 >> Evaluate the following improper integrals whenever they are convergent. Transcribed Image Text: ,00 fe6-3x dx.
Answer Preview: 00 e6 x dx lim dx lim fe6 3x dx b L…

, Chapter: 1 -Problem: 43 >> Let S(x) represent the total sales (in thousands of dollars) for the month x in the year 2005 at a certain department store. Represent each following statement by an equation involving S or S?. (a) The sales at the end of January reached $120,560 and were rising at the rate of $1500 per month. (b) At the end of March, the sales for this month dropped to $80,000 and were falling by about $200 a day
Answer Preview: a The sales at the end of January reached 120 560 s…

, Chapter: 11 -Problem: 3 >> Determine the third Taylor polynomial of the given function at x = 0.f(x) = 5e2x
Answer Preview: p3 r 5e20 …

, Chapter: 2 -Problem: 34 >> Let a, b, c, d be fixed numbers with a ? 0, and let f(x) = ax3 + bx2 + cx + d. Is it possible for the graph of f(x) to have more than one inflection point? Explain your answer.
Answer Preview: f x 3ax 2 2bx c f x 6…

, Chapter: 13 -Problem: 11 >> Express f (x) + g(x) as a rational function. Carry out all multiplications. Transcribed Image Text: f(x) = x + 5 x - 10' g(x)= = x + 10
Answer Preview: x 5 x 10 X …

, Chapter: 13 -Problem: 35 >> After t hours of operation, an assembly line has assembled A(t) = 20t - 1/2 t2 power lawn mowers, 0 ? t ? 10. Suppose that the factory’s cost of manufacturing x units is C(x) dollars, where C(x) = 3000 + 80x.(a) Express the factory’s cost as a (composite) function of the number of hours of operation of the assembly line.(b) What is the cost of the first 2 hours of operation?
Answer Preview: a b C A …

, Chapter: 10 -Problem: 12 >> If the function f (t) is a solution of the initial-value problem y? = et + y, y(0) = 0, find f (0) and f?(0).
Answer Preview: f 0 y 0 0 Si…

, Chapter: 2 -Problem: 12 >> Sketch the graph of a function that has the properties described.f(x) defined only for x ? 0; (0, 0) and (5, 6) are on the graph; f?(x) > 0 for x ? 0; f? (x) < 0 for x < 5, f??(5) = 0, f??(x) > 0 for x > 5.
Answer Preview: Y…

, Chapter: 10 -Problem: 24 >> Solve the initial-value problem.y? = 2(10 - y), y(0) = 1
Answer Preview: y 2 10 y y 0 1 y 20 2y y 2y 20 a …

, Chapter: 3 -Problem: 31 >> In Exercises, suppose that x and y are both differentiable functions of t and are related by the given equation. Use implicit differentiation with respect to t to determine dy/dt in terms of x, y, and dx/dt.x4 + y4 = 1
Answer Preview: x y 1 dx 4y3 …

, Chapter: 13 -Problem: 15 >> Determine the intercepts of the graphs of the following equations.x - 5y = 0
Answer Preview: x 5y 0 0 …

, Chapter: 6 -Problem: 38 >> Suppose that the velocity of a car at time t is y(t) = 40 + 8/(t + 1)2 kilometers per hour.(a) Compute the area under the velocity curve from t = 1 to t = 9.(b) What does the area in part (a) represent?
Answer Preview: a b The area represents the …

, Chapter: 2 -Problem: 17 >> Use the given information to make a good sketch of the function f(x) near x = 3. Transcribed Image Text: f(3) = ?2, ƒ'(3) = 2, ƒ"(3) = 3
Answer Preview: Y…

, Chapter: 9 -Problem: 50 >> The capital value of an asset such as a machine is sometimes defined as the present value of all future net earnings. The actual lifetime of the asset may not be known, and since some assets may last indefinitely, the capital value of the asset may be written in the formwhere r is the annual rate of interest compounded continuously.Suppose that a large farm with a known reservoir of gas beneath th
Answer Preview: Present value 10 000e0 04t …

, Chapter: 1 -Problem: 41 >> In Exercises, you are given a function and a point on the graph of the function. Zoom in on the graph at the given point until it starts to look like a straight line. Estimate the slope of the graph at the point indicated. Transcribed Image Text: f(x)=?x + 3, (1, 2).
Answer Preview: When x 1 y 2 Find a second poi…

, Chapter: 10 -Problem: 25 >> Solve the initial-value problem.y? + y = e2t, y(0) = -1
Answer Preview: y y et y 0 1 a t 1 b t et A t f …

, Chapter: 2 -Problem: 40 >> Sketch the following curves.y = x3 - 6x2 - 15x + 50
Answer Preview: y x6x 15x 50 y 3x 12x 15 y 6x 12 y 0 if x 1 or x 5 If x 1 y 58 If x 5 y 5…

, Chapter: 8 -Problem: 30 >> Differentiate (with respect to t or x):y = (cos t)ln t
Answer Preview: 1 cost In…

, Chapter: 13 -Problem: 2 >> What are the four types of inequalities, and what do they each mean?
Answer Preview: x y means x is less than y …

, Chapter: 13 -Problem: 34 >> Find the points of intersection of the pairs of curves.y = 3x2 + 9, y = 2x2 - 5x + 3
Answer Preview: Points of intersection …

, Chapter: 4 -Problem: 85 >> Use logarithmic differentiation to differentiate the following functions. Transcribed Image Text: f(x) = ex+¹(x² + 1)x
Answer Preview: 2 In f x In e x 1 x 2 x 1 ln …

, Chapter: 3 -Problem: 46 >> In Exercises, x and y are related by the given equation. Use implicit differentiation to calculate the value of dy/dx for the given values of x and y.xy2 - x3 = 10; x = 2, y = 3
Answer Preview: xy 2 x 3 10 y 2…

, Chapter: 13 -Problem: 21 >> Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = ?x. Find the following functions.f (x)h(x)
Answer Preview: f x h x …

, Chapter: 6 -Problem: 36 >> In Exercises, find the value of k that makes the antidifferentiation formula true. Transcribed Image Text: 5 2 - 3x S dx = k ln |2 - 3x + C
Answer Preview: d dx k …

, Chapter: 2 -Problem: 20 >> An athletic field [Fig. 8] consists of a rectangular region with a semicircular region at each end. The perimeter will be used for a 440-yard track. Find the value of x for which the area of the rectangular region is as large as possible. Transcribed Image Text: 8 Figure 8 h I I
Answer Preview: The objective is …

, Chapter: 10 -Problem: 3 >> Find an integrating factor for each equation. Take t > 0.t3y? + y = 0
Answer Preview: The integrating fa…

, Chapter: 1 -Problem: 45 >> In Exercises, use limits to compute f?(x). Transcribed Image Text: ?+ 7 + X^=(x)f
Answer Preview: f x x 2 f x lim h0 lim h0 f x h f x …

, Chapter: 10 -Problem: 27 >> A bank account has $20,000 earning 5% interest compounded continuously. A pensioner uses the account to pay himself an annuity, drawing continuously at a $2000 annual rate. How long will it take for the balance in the account to drop to zero?
Answer Preview: Let f t be the balance in the account after t years Then f t satisfies …

, Chapter: 2 -Problem: 40 >> The graph of each function in Exercises has one relative extreme point. Find it (giving both x- and y-coordinates) and determine if it is a relative maximum or a relative minimum point. Do not include a sketch of the graph of the function.f(x) = 30x2 - 1800x + 29,000
Answer Preview: Since f 30 is positive the graph is concave …

, Chapter: 8 -Problem: 35 >> Find the following indefinite integrals. Transcribed Image Text: [cos cos 2x dx
Answer Preview: cos c…

, Chapter: 13 -Problem: 2 >> Let f (x) = 2x + 3x2. Evaluate f (0), f ( - 1/4), and f (1>?2).
Answer Preview: f x 2x 3 x …

, Chapter: 13 -Problem: 31 >> The function f (r), which gives the cost (in cents) of constructing a 100-cubic-inch cylinder of radius r inches. The graph of f (r) is shown in Fig. 16.What is the additional cost of increasing the radius from 3 inches to 6 inches? Transcribed Image Text: 400 350 300 250 200 150 100 50 (1,330) (3,
Answer Preview: f 3 1 62 f …

, Chapter: 10 -Problem: 8 >> What is an integrating factor and how does it help you solve a first-order linear differential equation?
Answer Preview: An integrating factor is e A t where A t is an anti…

, Chapter: 4 -Problem: 83 >> Use logarithmic differentiation to differentiate the following functions. Transcribed Image Text: f(x) = Xex V?-3 x³ + 3
Answer Preview: xex mx he m x 3 mx xm …

, Chapter: 3 -Problem: 35 >> Find the point(s) on the graph of y = (x2 + 3x - 1)/x where the slope is 5.
Answer Preview: y dy dx 2 x 3x 1 X x 2…

, Chapter: 13 -Problem: 17 >> Compute the numbers.84/3
Answer Preview: 3 …

, Chapter: 6 -Problem: 24 >> Calculate the following integrals. Transcribed Image Text: ln 3 In 2 (ex + e)dx
Answer Preview: In 3 …

, Chapter: 2 -Problem: 16 >> Design an open rectangular box with square ends, having volume 36 cubic inches, that minimizes the amount of material required for construction.
Answer Preview: The objective is S 2x 2 3x…

, Chapter: 10 -Problem: 6 >> Use Euler’s method with n = 2 on the interval 2 ? t ? 3 to approximate the solution f (t) to y? = t - 2y, y(2) = 3. Estimate f (3).
Answer Preview: g t y t 2y y 2 …

, Chapter: 1 -Problem: 51 >> Each limit in Exercises is a definition of f?(a). Determine the function f(x) and the value of a. Transcribed Image Text: lim h?0 1 10+ h h -.1
Answer Preview: We want to find f x such th…

, Chapter: 11 -Problem: 3 >> Find the Taylor series at x = 0 of the given function by computing three or four derivatives and using the definition of the Taylor series.?1 + x
Answer Preview: The Taylor series …

, Chapter: 2 -Problem: 24 >> Each of the graphs of the functions in Exercises has one relative maximum and one relative minimum point. Plot these two points and check the concavity there. Using only this information, sketch the graph. Transcribed Image Text: f(x) = x³ + 2x² - 5x + ¾/ 13 8
Answer Preview: x x 2x 5x 1 3 8 3 f x x 4x 5 f x 2x …

, Chapter: 8 -Problem: 42 >> In any given locality, the length of daylight varies during the year. In Des Moines, Iowa, the number of minutes of daylight in a day t days after the beginning of a year is given approximately by the formula(a) Graph the function in the window [0, 365] by [-100, 940].(b) How many minutes of daylight are there on February 14, that is, when t = 45?(c) Use the fact that the value of the sine functio
Answer Preview: a b c The shortest amount of daylight will be when sine has the value 1 and the longest …

, Chapter: 13 -Problem: 13 >> LetandExpress the following as rational functions.f (x) - g(x) Transcribed Image Text: f(x) = X x-2' g(x)= 5-x 5 + x'
Answer Preview: X 5 xx 5 x…

, Chapter: 13 -Problem: 29 >> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions.g(x) - h(x - 3)
Answer Preview: g x h x 3 1 x 2 1 …

, Chapter: 2 -Problem: 11 >> Outline a method for locating the inflection points of a function.
Answer Preview: Solve f x 0 Let a solution be r…

, Chapter: 3 -Problem: 41 >> Computey = x2 - 3x, x = t2 + 3, t0 = 0 Transcribed Image Text: dy dt = to
Answer Preview: y x 3x x 1 3 to …

, Chapter: 13 -Problem: 16 >> LetandExpress the following as rational functions.g(x)h(x) Transcribed Image Text: f(x) = X x-2' g(x)= 5-x 5 + x'
Answer Preview: 5 x x …

, Chapter: 6 -Problem: 27 >> In Exercises, find the value of k that makes the antidifferentiation formula true. Transcribed Image Text: [264x=1dx=kets=1+ C
Answer Preview: e4x 1 …

, Chapter: 1 -Problem: 46 >> Using the sum rule and the constant-multiple rule, show that for any functions f(x) and g(x) Transcribed Image Text: dx [ƒ(x) = g(x)] = f(x) - d dx - d dx 86 g(x).
Answer Preview: d x g x x g x d dx dx d …

, Chapter: 10 -Problem: 27 >> Solve the following differential equations with the given initial conditions.y? = 5ty - 2t, y(0) = 1
Answer Preview: y 5ty 2t y 0 1 2 5 2 5 In y 2 …

, Chapter: 2 -Problem: 19 >> Properties of various functions are described next. In each case, draw some conclusion about the graph of the function. Transcribed Image Text: g(5) = ?1, g'(5) = ?2, g?(5) = 0
Answer Preview: Graph go…

, Chapter: 13 -Problem: 3 >> Use the quadratic formula to find the zeros of the functions.f (t) = 4t2 - 12t + 9
Answer Preview: f t 4t 12t 9 …

, Chapter: 1 -Problem: 34 >> In Exercises, apply the three-step method to compute f?(x) for the given function. Follow the steps that we used in Example 6. Make sure to simplify the difference quotient as much as possible before taking limits.Example 6Computing a Derivative from the Limit Definition Use limits to compute the derivative f?(5) for the following functions.
Answer Preview: f x x 2 Step 1 x h f x x …

, Chapter: 13 -Problem: 35 >> The cost and revenue functions in Fig. 17. The cost of producing x units of goods is C(x) dollars and the revenue from selling x units of goods is R(x) dollars.At what level of production is the cost $1400? Transcribed Image Text: 1800 1400 y 1000 600 y = R(x) y = C(x) Xx 10 20 30 40 50 60 70 Figure
Answer Preview: The cost …

, Chapter: 10 -Problem: 13 >> If f (t) is a solution of y? = (2 - y)e-y, is f (t) increasing or decreasing at some value of t where f (t) = 3?
Answer Preview: If f t y t 3 t…

, Chapter: 3 -Problem: 46 >> A closed rectangular box is to be constructed with one side 1 meter long. The material for the top costs $20 per square meter, and the material for the sides and bottom costs $10 per square meter. Find the dimensions of the box with the largest possible volume that can be built at a cost of $240 for materials.
Answer Preview: Let x be the length of the other side of the box and let h be its height Const…

, Chapter: 13 -Problem: 17 >> Factor the polynomials.3x2 + 12x + 12
Answer Preview: 3x 12x …

, Chapter: 6 -Problem: 37 >> An investment grew at an exponential rate R(t) = 700e0.07t + 1000, where t is in years and R(t) is in dollars per year. Approximate the net increase in value of the investment after the first 10 years (as t varies from 0 to 10).
Answer Preview: Let T t represent the value of the investment during a given time …

, Chapter: 2 -Problem: 15 >> Properties of various functions are described next. In each case, draw some conclusion about the graph of the function. Transcribed Image Text: h'(3) = 4, h"(3) = 1
Answer Preview: Increa…

, Chapter: 10 -Problem: 4 >> You are given a logistic equation with one or more initial conditions. (a) Determine the carrying capacity and intrinsic rate. (b) Sketch the graph of dN/dt versus N in an Nz-plane. (c) In the tN-plane, plot the constant solutions and place a dashed line where the concavity of certain solutions may change. (d) Sketch the solution curve corresponding to each given initial condition.dN/dt = -N2 + N,
Answer Preview: a carrying cap…

, Chapter: 1 -Problem: 44 >> (a) In Example 5, find the total sales for January 10, and determine the rate at which sales are falling on that day.(b) Compare the rate of change of sales on January 2 (Example 5) to the rate on January 10. What can you infer about the rate of change of sales? Example 5At the end of the holiday season in January, the sales at a department store are expected to fall (Fig. 3). It is estimated that
Answer Preview: a b Rate of change of sales on January 2 0 667 thousand day down 667 day Ra…

, Chapter: 2 -Problem: 23 >> Sketch the graphs of the following functions for x > 0. Transcribed Image Text: y X 1 + -X 4
Answer Preview: To find possible extrema set y 0 and solve for x Note that we need to consider the posi…

, Chapter: 8 -Problem: 28 >> Find t such that -?/2 ? t ? ?/2 and t satisfies the stated condition.sin t = sin(7?/6)
Answer Preview: sinf sin …

, Chapter: 13 -Problem: 6 >> Graph the following equations.y = 0
Answer Preview: y…

, Chapter: 13 -Problem: 30 >> Use the laws of exponents to compute the numbers.(31/3 · 31/6)6
Answer Preview: 31 3…

, Chapter: 10 -Problem: 9 >> In an autocatalytic reaction, one substance is converted into a second substance in such a way that the second substance catalyzes its own formation. This is the process by which trypsinogen is converted into the enzyme trypsin. The reaction starts only in the presence of some trypsin, and each molecule of trypsinogen yields 1 molecule of trypsin. The rate of formation of trypsin is proportional t
Answer Preview: y ky M y k 0 N …

, Chapter: 3 -Problem: 42 >> Suppose that in Boston the wholesale price, p, of oranges (in dollars per crate) and the daily supply, x (in thousands of crates), are related by the equation px + 7x + 8p = 328. If there are 4 thousand crates available today at a price of $25 per crate, and if the supply is changing at the rate of -.3 thousand crates per day, at what rate is the price changing?
Answer Preview: The price is increasing at the …

, Chapter: 13 -Problem: 16 >> Consider a rectangular corral with two partitions, as in Fig. 15. Assign letters to the outside dimensions of the corral. Write an equation expressing the fact that the corral has a total area of 2500 square feet. Write an expression for the amount of fencing needed to construct the corral (including both partitions). Tran
Answer Preview: lh …

, Chapter: 6 -Problem: 37 >> Find the area of the region bounded by the curves y = x3 - 3x + 1 and y = x + 1.
Answer Preview: Thus the graphs intersect …

, Chapter: 9 -Problem: 45 >> If k > 0, show that Transcribed Image Text: 00 S ke-kx dx = 1.
Answer Preview: ke kx dx lim bo So lim b…

, Chapter: 1 -Problem: 43 >> The line y = 2x + b is tangent to the graph of y = ?x at the point P = (a, ?a). Find P and determine b.
Answer Preview: The slope of the t…

, Chapter: 2 -Problem: 36 >> Sketch the following curves.y = 100 + 36x - 6x2 - x3
Answer Preview: f x 100 36x 6x x f x 36 12x 3 x f x 12 6x f x 0 if x 6 or x 2 f 6 116 6 116 …

, Chapter: 13 -Problem: 8 >> Consider the rectangle in Exercise 1. Write an expression for the area. Write an equation expressing the fact that the perimeter is 30 centimeters. Exercise 1Assign variables to the dimensions of the geometric object. Transcribed Image Text: Rectangle with height=3 width
Answer Preview: A …

, Chapter: 13 -Problem: 31 >> Sketch the graphs of the following functions.Sketch the parabola f (x) = 2x2 - 4x.
Answer Preview: f x 2x 4x a 2 b 4 …

, Chapter: 10 -Problem: 11 >> Suppose that the Consumer Products Safety Commission issues new regulations that affect the toy-manufacturing industry. Every toy manufacturer will have to make certain changes in its manufacturing process. Let f (t) be the fraction of manufacturers that have complied with the regulations within t months. Note that 0 ? f (t) ? 1. Suppose that the rate at which new companies comply with the regulat
Answer Preview: a y 1 1 y y 0 0 b Using Eulers method with n 3 h 1 …

, Chapter: 3 -Problem: 39 >> Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 2p3 + x2 = 4500. Determine the rate at which sales are changing at a time when x = 50, p = 10, and the price is falling at the rate of $.50 per week.
Answer Preview: The sales are rising at 3 thous…

, Chapter: 13 -Problem: 14 >> Factor the polynomials.x5 - x4 - 2x3
Answer Preview: r5 x …

, Chapter: 6 -Problem: 32 >> Find the volume of the solid of revolution generated by revolving about the x-axis the region under each of the following curves.y = kx from x = 0 to x = h
Answer Preview: ih 7 …

, Chapter: 10 -Problem: 1 >> Suppose that f (t) is a solution of the differential equation y? = ty - 5 and the graph of f (t) passes through the point (2, 4). What is the slope of the graph at this point?
Answer Preview: The slo…

, Chapter: 1 -Problem: 53 >> Each limit in Exercises is a definition of f?(a). Determine the function f(x) and the value of a. Transcribed Image Text: lim h?0 ?9+h-3 h
Answer Preview: We want to find f x such t…

, Chapter: 11 -Problem: 14 >> Find the Taylor series at x = 0 of the given function. Use suitable operations (differentiation, substitution, etc.) on the Taylor series at x = 0 of3(e-2x - 2) Transcribed Image Text: 1 1- x 9 et, or cos x.
Answer Preview: 36 2 21 3 6 2 …

, Chapter: 2 -Problem: 29 >> Find the point on the graph of y = ?x that is closest to the point (2, 0). See Fig. 17. Transcribed Image Text: 2 1 0 Y 2 y = {x +x 3 1 Figure 17 Shortest distance from a point to a curve. 8
Answer Preview: By the …

, Chapter: 13 -Problem: 1 >> Use the quadratic formula to find the zeros of the functions.f(x) = 2x2 - 7x + 6
Answer Preview: f x 2x 7x 6 2x …

, Chapter: 13 -Problem: 28 >> The function f (r), which gives the cost (in cents) of constructing a 100-cubic-inch cylinder of radius r inches. The graph of f (r) is shown in Fig. 16.For what value(s) of r is the cost 330 cents? Transcribed Image Text: 400 350 300 250 200 150 100 50 (1,330) (3, 162) (6.87, 330) y = f(r) 0 1 2 3
Answer Preview: From the …

, Chapter: 3 -Problem: 30 >> Find the equation of the tangent line to the curve y = (x + 1)/(x - 1) at the point (2, 3).
Answer Preview: x 1 x 1 y dy x 1 1 …

, Chapter: 13 -Problem: 16 >> State the six laws of exponents.
Answer Preview: bbs 6 s b …

, Chapter: 6 -Problem: 34 >> Suppose that the marginal profit function for a company is P?(x) = 100 + 50x - 3x2 at production level x.(a) Find the extra profit earned from the sale of 3 additional units if 5 units are currently being produced.(b) Describe the answer to part (a) as an area.
Answer Preview: a b It is the area under …

, Chapter: 2 -Problem: 15 >> In the planning of a sidewalk café, it is estimated that for 12 tables, the daily profit will be $10 per table. Because of overcrowding, for each additional table the profit per table (for every table in the café) will be reduced by $.50. How many tables should be provided to maximize the profit from the café?
Answer Preview: Let P x be the profit from x table…

, Chapter: 10 -Problem: 5 >> State the order of the differential equation and verify that the given function is a solution. Transcribed Image Text: (11²)y" - 2ty' + 2y = 0, y(t) = t
Answer Preview: The highest derivative is t…

, Chapter: 1 -Problem: 48 >> Figure 3 contains the curves y = f (x), y = g(x), and y = h(x) and the tangent lines to y = f (x) and y = g(x) at x = 1, with h(x) = f(x) + g(x). Find h(1) and h?(1). Transcribed Image Text: Y y = h(x) y = f(x) y = 4x + 2.6 y .26x + 1.1 1 Figure 3 Graphs of f(x), g(x), and h(x) = f(x) + g(x). y = g(
Answer Preview: h 1 f 1 g …

, Chapter: 11 -Problem: 2 >> Find the Taylor series at x = 0 of the given function by computing three or four derivatives and using the definition of the Taylor series.ln(1 - 3x)
Answer Preview: f x ln 1 3x f x f x 3 12 …

, Chapter: 2 -Problem: 26 >> Sketch the following curves, indicating all relative extreme points and inflection points.y = x3 - 6x2 + 9x + 3
Answer Preview: Concavity reverses between x 1 and x 3 so ther…

,

, Chapter: 1 -Problem: 30 >> Do Exercise 29 if it costs 10 cents per copy for the first 50 copies and 5 cents per copy for each copy exceeding 50, and there is no setup fee. Exercise 29The owner of a photocopy store charges 7 cents per copy for the first 100 copies and 4 cents per copy for each copy exceeding 100. In addition, there is a setup fee of $2.50 for each photocopying job.(a) Determine R(x), the revenue from selling
Answer Preview: a All together we have b L…

, Chapter: 10 -Problem: 10 >> A porous material dries outdoors at a rate that is proportional to the moisture content. Set up the differential equation whose solution is y = f (t), the amount of water at time t in a towel on a clothesline. Sketch the solution.
Answer Preview: y ky k 0 …

, Chapter: 3 -Problem: 35 >> In Exercises, suppose that x and y are both differentiable functions of t and are related by the given equation. Use implicit differentiation with respect to t to determine dy/dt in terms of x, y, and dx/dt.x2 + 2xy = y3
Answer Preview: x 2xy y dy 2 x …

, Chapter: 13 -Problem: 23 >> LetandExpress the following as rational functions. Transcribed Image Text: f(x) = X x-2' g(x)= 5-x 5 + x'
Answer Preview: 1 5 5u 1 …

, Chapter: 9 -Problem: 7 >> Approximate the following integrals by the midpoint rule; then, find the exact value by integration. Express your answers to five decimal places. Transcribed Image Text: f (x² + 5)dx; n = 2,4 2
Answer Preview: Evaluating the integral directly we have 4 0 2 2 The first mi…

, Chapter: 6 -Problem: 31 >> A rock is dropped from the top of a 400-foot cliff. Its velocity at time t seconds is y(t) = -32t feet per second. Find the displacement of the rock during the time interval 2 ? t ? 4.
Answer Preview: Let s t represent the position functi…

, Chapter: 2 -Problem: 49 >> A car is traveling on a straight road and s(t) is the distance traveled after t hours. Match each set of information about s(t) and its derivatives with the corresponding description of the car’s motion.InformationA. s(t) is a constant function.B. s(t) is a positive constant function.C. s(t) is positive at t = a.D. s(t) is negative at t = a.E. s(t) and s(t) are positive at t = a.F. s(t) is p
Answer Preview: A c …

, Chapter: 1 -Problem: 53 >> When the owner of a gas station sets the price of 1 gallon of unleaded gasoline at $2.10, she can sell approximately 1500 gallons per day. When she sets the price at $2.25 per gallon, she can sell approximately 1250 gallons per day. Let G(x) denote the number of gallons of unleaded gasoline sold per day when the price is x dollars. Assume that G(x) is a linear function of x. Approximately how many
Answer Preview: The points 2 10 1500 and 2 25 1250 ar…

, Chapter: 11 -Problem: 2 >> Determine the sums of the following geometric series when they are convergent. Transcribed Image Text: 1 + + 3|4 + 3|4 + ele + 4
Answer Preview: 3 The series …

, Chapter: 2 -Problem: 25 >> Sketch the following parabolas. Include their x- and y-intercepts.y = x2 + 3x - 10
Answer Preview: y x 3x 10 y 2x 3 y 2 3 y 0 if x 2 49 49 If …

, Chapter: 13 -Problem: 4 >> Compute the numbers.025
Answer Preview: 0…

, Chapter: 1 -Problem: 28 >> Differentiate.f(x) = (2x + 1)3
Answer Preview: f x 2…

, Chapter: 10 -Problem: 17 >> One or more initial conditions are given for each differential equation in the following exercises. Use the qualitative theory of autonomous differential equations to sketch the graphs of the corresponding solutions. Include a yz-graph if one is not already provided. Always indicate the constant solutions on the ty-graph whether they are mentioned or not. y? = g(y), y(0) = -.5, y(0) = .5, where g(
Answer Preview: 5 …

, Chapter: 3 -Problem: 49 >> Let R(x) be the revenue received from the sale of x units of a product. The average revenue per unit is defined by AR = R(x)/x. Show that at the level of production where the average revenue is maximized, the average revenue equals the marginal revenue.
Answer Preview: Recall that the marginal revenue MR is …

, Chapter: 13 -Problem: 25 >> Letand h(x) = x3 - 5x2 + 1. Calculate the following functions.f (g(x)) Transcribed Image Text: 1 ? x' (x)8'9x = (x) f
Answer Preview: X …

, Chapter: 9 -Problem: 12 >> Approximate the following integrals by the trapezoidal rule; then, find the exact value by integration. Express your answers to five decimal places. Transcribed Image Text: 1 4 x-3 -dx; n = 5
Answer Preview: 1de dx x 3 do Using the trapezoidal rule with …

, Chapter: 6 -Problem: 35 >> Find the volume of the solid of revolution generated by revolving about the x-axis the region under each of the following curves.y = 2x + 1 from x = 0 to x = 1
Answer Preview: 7 2x 1 dx 7 …

, Chapter: 1 -Problem: 42 >> Refer to Exercise 41. Is it profitable to produce 1300 chips per day if the cost of producing 1200 chips per day is $14,000? Exercise 41Let R(x) denote the revenue (in thousands of dollars) generated from the production of x units of computer chips per day, where each unit consists of 100 chips.
Answer Preview: Since C 12 14 and R 12 22 t…

, Chapter: 10 -Problem: 28 >> Solve the following differential equations with the given initial conditions. Transcribed Image Text: y' = y , y(0) = -5
Answer Preview: y 1 y y 1 y dy tdt dy dt 73 y …

, Chapter: 2 -Problem: 28 >> Sketch the graphs of the following functions for x > 0. Transcribed Image Text: I + -12 y
Answer Preview: To find possible extrema set y 0 and s…

, Chapter: 13 -Problem: 6 >> Let f (x) = x2 + 1, g(x) = 9x, and h(x) = 5 - 2x2. Calculate the following functions.g(t)/h(t)
Answer Preview: g t…

, Chapter: 5 -Problem: 2 >> Consider the function g(x) = 10 - 10e-0.1x, x ? 0.(a) Show that g(x) is increasing and concave down for x ? 0.(b) Explain why g(x) approaches 10 as x gets large.(c) Sketch the graph of g(x), x ? 0.
Answer Preview: a b …

, Chapter: 1 -Problem: 18 >> Find an equation of the given line.Slope is 2; x-intercept is -3
Answer Preview: Slope 2 x intercept …

, Chapter: 10 -Problem: 7 >> Solve the differential equations in Exercises.yy? + t = 6t2, y(0) = 7
Answer Preview: 2 yy t 6t y 0 7 Sy d…

, Chapter: 3 -Problem: 33 >> In Exercises, suppose that x and y are both differentiable functions of t and are related by the given equation. Use implicit differentiation with respect to t to determine dy/dt in terms of x, y, and dx/dt.3xy - 3x2 = 4
Answer Preview: 4 dy dt 3 xy 3x …

, Chapter: 13 -Problem: 14 >> What is a zero of a function?
Answer Preview: x a i…

, Chapter: 9 -Problem: 1 >> Determine if the given expression approaches a limit as b ? ?, and find that number when it does.5/b
Answer Preview: As b…

, Chapter: 6 -Problem: 25 >> Calculate the following integrals. Transcribed Image Text: In 3 S et + e e²x X dx
Answer Preview: Ine…

, Chapter: 2 -Problem: 18 >> Refer to the graph in Fig. 20.(a) At which labeled points is the function decreasing?(b) At which labeled points is the graph concave down?(c) Which labeled point has the most negative slope (that is, negative and with the greatest magnitude)? Transcribed Image Text: Figure 20 y A B D E F 'y = f(x)
Answer Preview: a …

, Chapter: 1 -Problem: 50 >> The discovery of one case of bovine spongiform encephalopathy, or mad cow disease, in May 2003 in Canada led to an immediate ban on all Canadian beef exports. At the beginning of September 2003, the ban was lifted, and exports of Canadian beef rose at a steady rate of $42.5 million per month. Express the value of the monthly exports of Canadian beef as a function of time for the period starting th
Answer Preview: Let y be the value of monthly exports in millions of do…

, Chapter: 11 -Problem: 3 >> Determine the sums of the following geometric series when they are convergent. Transcribed Image Text: 1 - 1 3² + 1 1 1 34 36 38 +
Answer Preview: 1 a 1…

, Chapter: 2 -Problem: 33 >> Sketch the following curves.y = 2x3 + 3x2 + 1
Answer Preview: f x 2x 3x 1 f x 6x 6x f x 12x 6 f x 0 if x 0 or x 1 f 0 1 0 1 is a …

, Chapter: 13 -Problem: 14 >> Factor the polynomials.x2 - 10x + 16
Answer Preview: 10…

, Chapter: 1 -Problem: 32 >> A supermarket finds that its average daily volume of business, V (in thousands of dollars), and the number of hours, t, that the store is open for business each day are approximately related by the formula Transcribed Image Text: Find dV dt V = 20 (1 t=10 100 72). 100+ t 0?t? 24.
Answer Preview: V 20 1 dV V 20 2000 100 …

, Chapter: 5 -Problem: 2 >> Let A(t) be the balance in a savings account after t years, and suppose that A(t) satisfies the differential equation A?(t) = .045A(t), A(0) = 3000.(a) How much money was originally deposited in the account?(b) What interest rate is being earned?(c) Find the formula for A(t).(d) What is the balance after 5 years?(e) Use part (d) and the differential equation to determine how fast the balance is gr
Answer Preview: a 3000 b 045 4 5 c A t 3…

, Chapter: 1 -Problem: 26 >> Refer to Fig. 13. Do you agree with the statement that the price of one barrel of crude oil fell on July 1, 2015, and on December 1, 2015, at approximately the same rate? Justify your answer. Transcribed Image Text: $/Barrel y $95 $85 $ 75 $ 65 $ 55 $45 $35 $25 March May July Sep. 2015 2015 2015 20
Answer Preview: Yes the slo…

, Chapter: 3 -Problem: 47 >> A sugar refinery can produce x tons of sugar per week at a weekly cost of .1x2 + 5x + 2250 dollars. Find the level of production for which the average cost is at a minimum and show that the average cost equals the marginal cost at that level of production.
Answer Preview: Let AC x be the average cost of producing x units and let C x be the tot…

, Chapter: 13 -Problem: 21 >> Let f (x) be the cost–benefit function. If 70% of the pollutant has been removed, what is the added cost to remove another 5%? How does this compare with the cost to remove the final 5% of the pollutant?
Answer Preview: we know that f 70 100 The cost to remove 75 of the polluta…

, Chapter: 9 -Problem: 7 >> A growth company is one whose net earnings tend to increase each year. Suppose that the net earnings of a company at time t are being generated at the rate of 30 + 5t million dollars per year.(a) Write a definite integral that gives the present value of the company’s earnings over the next 2 years using a 10% interest rate.(b) Compute the present value described in part (a).
Answer Preview: a b K t 30…

, Chapter: 6 -Problem: 33 >> Find the volume of the solid of revolution generated by revolving about the x-axis the region under each of the following curvesy = ?x from x = 0 to x = 4
Answer Preview: 2 4 7…

, Chapter: 2 -Problem: 20 >> Sketch the graphs of the following functions.f(x) = 3x4 - 6x2 + 3
Answer Preview: To find possible extrema set f x 0 and solve for x …

, Chapter: 1 -Problem: 40 >> In Exercises, find an equation of the tangent line to the graph of y = f (x) at the given x. Do not apply formula (6), but proceed as we did in Example 4. Example 4.Finding the Equation of the Tangent Line at a Given x Find the point–slope equation of the tangent line to the graph of Transcribed Image Text:
Answer Preview: For exercises refer to Example 4 on page 77 in the te…

, Chapter: 2 -Problem: 28 >> Sketch the following parabolas. Include their x- and y-intercepts.y = x2 - 9x + 19
Answer Preview: y x 9x 19 y 2x 9 2 y 0 if x If x 2 y so 2 2 …

, Chapter: 13 -Problem: 2 >> Let f (x) = x2 + 1, g(x) = 9x, and h(x) = 5 - 2x2. Calculate the following functions.f (x) - h(x)
Answer Preview: f x …

, Chapter: 5 -Problem: 23 >> Investment A is currently worth $70,200 and is growing at the rate of 13% per year compounded continuously. Investment B is currently worth $60,000 and is growing at the rate of 14% per year compounded continuously. After how many years will the two investments have the same value?
Answer Preview: A t 70 200e0 13 B t 60 000e0 Set …

, Chapter: 1 -Problem: 24 >> Determine which of the following limits exist. Compute the limits that exist. Transcribed Image Text: lim x-7 x³ - 2x² + 3x .2
Answer Preview: lim X7 3 x 2x 3…

, Chapter: 13 -Problem: 38 >> Simplify (100)3/2 and (.001)1/3.
Answer Preview: 3 100 …

, Chapter: 3 -Problem: 43 >> In Exercises, x and y are related by the given equation. Use implicit differentiation to calculate the value of dy/dx for the given values of x and y.x2y2 = 9; x = 1, y = 3
Answer Preview: x 2 y 2 9 2 …

, Chapter: 13 -Problem: 15 >> Compute the numbers.(.01)-1
Answer Preview: 0…

, Chapter: 9 -Problem: 10 >> Determine the integrals in Exercises by making appropriate substitutions. Transcribed Image Text: f(x³3-6 - 6x)7(x² - 2)dx
Answer Preview: f x 6x 7 x 2 dx Let …

, Chapter: 6 -Problem: 22 >> Find the area under each of the given curves.y = ?x; x = 0 to x = 4
Answer Preview: So x dx …

, Chapter: 2 -Problem: 16 >> Each of the graphs of the functions in Exercises has one relative extreme point. Plot this point and check the concavity there. Using only this information, sketch the graph. [Recall that if f (x) = ax2 + bx + c, then f(x) has a relative minimum point when a > 0 and a relative maximum point when a < 0.]f(x) = -x2 + 2x - 5
Answer Preview: f x x 2x 5 f …

, Chapter: 10 -Problem: 7 >> Is the constant function f (t) = 3 a solution of the differential equation y? = 6 - 2y?
Answer Preview: Yes G…

, Chapter: 1 -Problem: 47 >> (a) Let A(x) denote the number (in hundreds) of computers sold when x thousand dollars is spent on advertising. Represent the following statement by equations involving A or A?: When $8000 is spent on advertising, the number of computers sold is 1200 and is rising at the rate of 50 computers for each $1000 spent on advertising.(b) Estimate the number of computers that will be sold if $9000 is spen
Answer Preview: a When 8000 is spent on advertising 1200 computers were …

, Chapter: 11 -Problem: 12 >> Use the Newton–Raphson algorithm to find an approximate solution to e5-x = 10 - x.
Answer Preview: f x e5 x x 10 f x e5 x 1 There …

, Chapter: 2 -Problem: 27 >> Sketch the graphs of the following functions for x > 0. Transcribed Image Text: y || + To N +2
Answer Preview: To find possible extrema set y 0 and s…

, Chapter: 12 -Problem: 11 >> A random variable X has a uniform density function f (x) = 1/5 on 20 ? x ? 25.(a) Find E (X ) and Var (X ).(b) Find b such that Pr (X ? b) = .3.
Answer Preview: a b 125 E X 25 1 …

, Chapter: 13 -Problem: 12 >> What is meant by the absolute value of a number?
Answer Preview: f x x i…

, Chapter: 1 -Problem: 29 >> Compute the following. Transcribed Image Text: d dv dt dt t=2 where v(t) = 31³ + 4 t
Answer Preview: d dv du where v t 3t 4 …

, Chapter: 13 -Problem: 56 >> Compute f (1), f (2), and f (3). Transcribed Image Text: 3/(4x) f(x) = 2x ??²-5 for x < 2 for 2 for 3 ? x x < 3
Answer Preview: f x 3 4 x 2x …

, Chapter: 10 -Problem: 22 >> One or more initial cond

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