Description

Chapter: 1 -Problem: 11 >> A city’s population was 28,600 in the year 2015 and is growing by 750 people a year. (a) Give a formula for the city’s population, P, as a function of the number of years, t, since 2015. (b) What is the population predicted to be in 2020? (c) When is the population expected to reach 35,000?
Answer Preview: a The slope is constant at 750 people per year so this is a linear function …

, Chapter: 4 -Problem: 3 >> Problem are about chikungunya, a disease that arrived in the Americas in 2013 and spread rapidly in 2014. While seldom fatal, the disease causes debilitating joint pain and a high fever. In August 2014, a public challenge was issued to predict the number of cases in each of the affected countries. The winners, Joceline Lega and Heidi Brown, used a logistic model to make their predictions. Let N be
Answer Preview: The continuous growth rate for small P i…

, Chapter: 6 -Problem: 87 >> Find an antiderivative and use differentiation to check your answer.q(x) = 7 sin x ? sin(7x)
Answer Preview: 7 cos …

, Chapter: 1 -Problem: 38 >> Linear supply and demand curves are shown in Figure 1.66, with price on the vertical axis. (a) Label the equilibrium price p0 and the equilibrium quantity q0 on the axes. (b) Explain the effect on equilibrium price and quantity if the slope, ?p??q, of the supply curve increases. Illustrate your answer graphically. (c) Explain the effect on equilibrium price and quantity if the slope, ?p??q, of the
Answer Preview: (a) See Figure 1 37. (b) If the slope of the supply curve increases then the supply curv…

, Chapter: 4 -Problem: 14 >> A developer has purchased a laundromat and an adjacent factory. To keep smoke, which ruins the clothes, out of the dryers the developer can protect the laundromat or install filters on the factory’s smokestacks. The daily cost of filters for the factory and the cost of protecting the laundromat against smoke depend on the number of filters used, as shown in the the table. (a) Make a table which sh
Answer Preview: a The costs and savings are in Table 4 1 b She should install four filters Up to the fourth filter t…

, Chapter: 6 -Problem: 2 >> Find the integrals in Problems. Transcribed Image Text: pe pe-0.1p dp
Answer Preview: Let u p and v e 0 1 p …

, Chapter: 5 -Problem: 1 >> You travel 30miles/hour for 2 hours, then 40miles/hour for 1?2 hour, then 20 miles/hour for 4 hours. (a) What is the total distance you traveled? (b) Sketch a graph of the velocity function for this trip. (c) Represent the total distance traveled on your graph in part (b).
Answer Preview: a We compute the distances traveled for each of the three legs of the trip and add them to find the …

, Chapter: 8 -Problem: 6 >> Values of f(x, y) and its derivatives are given in Table 8.13. (a) Identify which points in Table 8.13 are critical points of f. (b) For each critical point, determine whether it is a local minimum, maximum, or saddle point. Transcribed Image Text: Table 8.13 Values of f and its derivatives (x, y) y
Answer Preview: a Critical points of f occur at points where each of the partial derivatives are either …

, Chapter: 6 -Problem: 42 >> For Problems show the following quantities on Figure 6.22.A slope representing f(b) ? f(a) /b ? a. Transcribed Image Text: a f(x) b Figure 6.22 X
Answer Preview: See Figure 6 …

, Chapter: 3 -Problem: 36 >> (a) Use Figure 3.18 to rank the quantities f'(1), f'(2), f'(3) from smallest to largest. (b) Confirm your answer by calculating the quantities using the formula, f(x) = 2ex ? 3x2?x. Transcribed Image Text: 8 4 -4 -8 1 3 Figure 3.18 f(x) + x 4
Answer Preview: a The slope of f appears to be positive at x 3 so f 3 0 On the other hand …

, Chapter: 2 -Problem: 32 >> For Problem estimate the change in y for the given change in x.y = f(x), f'(12) = 30, x increases from 12 to 12.2
Answer Preview: We have …

, Chapter: 5 -Problem: 36 >> Figure 5.67 shows plasma concentration curves for two products containing a drug used to slow a rapid heart rate. Compare the two products in terms of level of peak concentration, time until peak concentration, and overall exposure. Which product should be used to achieve the fastest response? Transcribed Image Text:
Answer Preview: We see that Product B gives a greater peak concentration …

, Chapter: 1 -Problem: 26 >> A quantity P is an exponential function of time t. Use the given information about the function P = P0at to:(a) Find values for the parameters a and P0. (b) State the initial quantity and the percent rate of growth or decay.P0a4 = 18 and P0a3 = 20
Answer Preview: a We divide the two equations to solve for a Now that we know …

, Chapter: 8 -Problem: 20 >> Sketch a contour diagram for the function with at least four labeled contours. Describe in words the contours and how they are spaced.f(x, y) = xy
Answer Preview: The contour where f x y xy c is …

, Chapter: 3 -Problem: 53 >> Carbon-14 is a radioactive isotope used to date objects. If A0 represents the initial amount of carbon-14 in the object, then the quantity remaining at time t, in years, isA(t) = A0e?0.000121t.(a) A tree, originally containing 185 micrograms of carbon-14, is now 500 years old. At what rate is the carbon-14 decaying now? (b) In 1988, scientists found that the Shroud of Turin, which was reputed to b
Answer Preview: a We first substitute A 0 185 differentiate A t and substitute t 500 A t 185e 0 000121t A t …

, Chapter: 7 -Problem: 21 >> While taking a walk along the road where you live, you accidentally drop your glove, but you don’t know where. The probability density p(x) for having dropped the glove x kilometers from home (along the road) isp(x) = 2e?2x for x ? 0.(a) What is the probability that you dropped it within 1 kilometer of home? (b) At what distance y from home is the probability that you dropped it within y km of hom
Answer Preview: a The probability you dropped the glove …

, Chapter: 4 -Problem: 4 >> Problem are about chikungunya, a disease that arrived in the Americas in 2013 and spread rapidly in 2014. While seldom fatal, the disease causes debilitating joint pain and a high fever. In August 2014, a public challenge was issued to predict the number of cases in each of the affected countries. The winners, Joceline Lega and Heidi Brown, used a logistic model to make their predictions. Let N be
Answer Preview: To find the initial number of cases from the formula we …

, Chapter: 6 -Problem: 11 >> Figure 6.7 shows the derivative g'. If g(0) = 0, graph g. Give (x, y)-coordinates of all local maxima and minima. Transcribed Image Text: - 2 3 ??? -g'(x)- + Figure 6.7 5 6 x
Answer Preview: First we observe that g is increasing when g is positive which is when 0 x 4 g is decreasing when g …

, Chapter: 6 -Problem: 7 >> Let F(x) be an antiderivative of f(x), with F(1) = 20 and ?41 f(x) dx = ?7. What is F(4)?
Answer Preview: The Fundamental The…

, Chapter: 2 -Problem: 21 >> Match the functions in Problem with one of the derivatives in Figure 2.29. Transcribed Image Text: (III) E 3 (M) (VII) -5 15+ 2 -5+ 5+ f'(x) ƒ'(x) x x (10) (M) (VI) (MI) -5 Figure 2.29 -5+ 5+ -5+ 5 f'(x) -5+ 5+ f'(x) x f'(x) f'(x) x
Answer Preview: The function is increasing for x 2 and decreasing for x 2 The corresponding derivative is positive …

, Chapter: 8 -Problem: 18 >> The monthly cost, in dollars, of a cell phone bill isP = f(t, m, d) = 0.25t + 0.2m + 0.01dwhere t is the number of minutes talked, m is the number of messages sent and d is the number of kilobytes of data used that month. (a) Find f(250, 200, 100) and interpret it. (b) Find a formula for monthly cost if your data is disabled. (c) You are considering switching to an unlimited talk, text and data pl
Answer Preview: a f 250 200 100 0 25 250 0 2 200 0 01 100 103 5 Talking for 250 minutes sending 200 texts and …

, Chapter: 3 -Problem: 17 >> Find the derivative of the functions in Problems.f(x) = ln(ex + 1)
Answer Preview: f …

, Chapter: 2 -Problem: 56 >> A person with a certain liver disease first exhibits larger and larger concentrations of certain enzymes (called SGOT and SGPT) in the blood. As the disease progresses, the concentration of these enzymes drops, first to the pre-disease level and eventually to zero (when almost all of the liver cells have died). Monitoring the levels of these enzymes allows doctors to track the progress of a patien
Answer Preview: a See part b b See Figure 2 28 c The derivative f is the rate at which the concen…

, Chapter: 8 -Problem: 19 >> Maximize production, Q = 5x0.3y0.8, where x and y are quantities of raw materials and the total quantity of these raw materials cannot be more than 100.
Answer Preview: Let g x y x y Then the constraint is g x y x y 100 At the maximum Dividing t…

, Chapter: 5 -Problem: 23 >> Use an integral to find the specified area. Under y = 5 ln(2x) and above y = 3 for 3 ? x ? 5.
Answer Preview: The graph of y 5 ln 2x is abov…

, Chapter: 3 -Problem: 47 >> Use the tangent line approximation.Given f(x) = x3 + x2 ? 6, approximate f(0.97).
Answer Preview: We have x 0 97 1 0 03 D…

, Chapter: 4 -Problem: 7 >> Would you expect the demand for high-definition television sets to be elastic or inelastic? Explain.
Answer Preview: Demand for high-definition TVs will be el…

, Chapter: 3 -Problem: 46 >> A patient’s total cholesterol level, T (t), and good cholesterol level, G(t), at t weeks after January 1, 2016, are measured in milligrams per deciliter of blood (mg/dl). The cholesterol ratio, R(t) = G(t)?T (t), is used to gauge the safety of a patient’s cholesterol, with risk of cholesterol-related illnesses being minimized when R(t) > 1?5 (that is, good cholesterol is at least 1?5 of total chol
Answer Preview: a Even though the total cholesterol increases it is possibl…

, Chapter: 3 -Problem: 20 >> Find the derivative of the functions in Problems.f(x) = (ln x)3
Answer Preview: If we let z ln …

, Chapter: 2 -Problem: 25 >> Let G be annual US government purchases, T be annual US tax revenues, and Y be annual US output of all goods and services. All three quantities are given in dollars. Interpret the statements about the two derivatives, called fiscal policy multipliers. (a) dY ?dG = 0.60 (b) dY ?dT = ?0.26
Answer Preview: a An additional dollar per year of government purchases …

, Chapter: 8 -Problem: 2 >> Use Lagrange multipliers to find the maximum or minimum values of f(x, y) subject to the constraint.f(x, y) = x2 + 4xy, x + y = 100
Answer Preview: We wish to optimize f x y x 2 4xy subject to the constraint g …

, Chapter: 3 -Problem: 37 >> Find the derivative. Assume a, b, c, k are constants. Transcribed Image Text: h(x) = ax + b ?
Answer Preview: Since h …

, Chapter: 2 -Problem: 33 >> Which of the functions described in Problems are continuous?You start in North Carolina and go westward on Interstate 40 toward California. Consider the function giving the local time of day as a function of your distance from your starting point.
Answer Preview: The time is not a continuous funct…

, Chapter: 1 -Problem: 29 >> A health club has cost and revenue functions given by C = 10,000 + 35q and R = pq, where q is the number of annual club members and p is the price of a one year membership. The demand function for the club is q = 3000 ? 20p. (a) Use the demand function to write cost and revenue as functions of p. (b) Graph cost and revenue as a function of p, on the same axes. (c) Explain why the graph of the reve
Answer Preview: a We know that b The graph of the cost and revenue functions are shown in Figure 1 81 c It makes sen…

, Chapter: 3 -Problem: 74 >> A ball is dropped from the top of the Empire State Building. The height, y, of the ball above the ground (in feet) is given as a function of time, t (in seconds), byy = 1250 ? 16t2.(a) Find the velocity of the ball at time t. What is the sign of the velocity? Why is this to be expected? (b) When does the ball hit the ground, and how fast is it going at that time? Give your answer in feet per secon
Answer Preview: a Velocity v t dy dt d dt 1250 16t 2 32t Since t 0 the balls velocity is negativ…

, Chapter: 4 -Problem: 7 >> Let C(q) represent the cost, R(q) the revenue, and (q) the total profit, in dollars, of producing q items. (a) If C'(50) = 75 and R'(50) = 84, approximately how much profit is earned by the 51st item? (b) If C'(90) = 71 and R'(90) = 68, approximately how much profit is earned by the 91st item? (c) If (q) is a maximum when q = 78, how do you think C'(78) and R'(78) compare? Explain.
Answer Preview: (a) The profit earned by the 51 st is the revenue earned by the 51 st ite…

, Chapter: 3 -Problem: 38 >> For t in years since 2010, daily oil consumption in China, in thousands of barrels, was approximated byB = 8938e0.05t.(a) Is daily oil consumption increasing or decreasing with time? (b) How fast is oil consumption changing at time t?
Answer Preview: a Since B 8938e 0 05t an exponential function with rate …

, Chapter: 6 -Problem: 15 >> Decide whether the expression is a number or a family of functions. (Assume f(x) is a function.) Transcribed Image Text: +²) dx x
Answer Preview: Since the e…

, Chapter: 3 -Problem: 7 >> For Problems find the derivative. Assume a, b, c, k are constants.y = 5x + 13
Answer Preview: d…

, Chapter: 8 -Problem: 13 >> The function has a critical point at (0, 0). What sort of critical point is it?f(x, y) = x2 ? cos y
Answer Preview: We have f x 2x and f y sin y so f xx 2 …

, Chapter: 3 -Problem: 18 >> Find the derivative. Assume a, b, c, k are constants. Transcribed Image Text: g(t) =
Answer Preview: Since g …

, Chapter: 1 -Problem: 29 >> A company produces and sells shirts. The fixed costs are $7000 and the variable costs are $5 per shirt.(a) Shirts are sold for $12 each. Find cost and revenue as functions of the quantity of shirts, q.(b) The company is considering changing the selling price of the shirts. Demand is q = 2000 ? 40p, where p is price in dollars and q is the number of shirts. What quantity is sold at the current pric
Answer Preview: a We know that the cost function will be of the form C mq b where m is the variable cost and b is th…

, Chapter: 3 -Problem: 46 >> Use Figure 3.22 to evaluate the derivative. Transcribed Image Text: 80 0 # f(x) 80 $6 0 Figure 3.22 80
Answer Preview: The chain rul…

, Chapter: 6 -Problem: 55 >> Use integration by substitution and the Fundamental Theorem to evaluate the definite integrals in Problems. Transcribed Image Text: -3 10 Vt + 1 dt
Answer Preview: We substitute w t 1 …

, Chapter: 4 -Problem: 12 >> Graph a function with the given properties.Has no local or global maxima or minima.
Answer Preview: y F…

, Chapter: 4 -Problem: 16 >> In Kazakhstan, the demand curve 12 of dairy products is q = kp?0.6 for some positive constant k. What is the elasticity of dairy products in Kazakhstan?
Answer Preview: We have E p …

, Chapter: 3 -Problem: 28 >> Find and interpret the value of the expression in practical terms. Let C(t) be the concentration of carbon dioxide in parts per million (ppm) in the air as a function of time, t, in months since December 1, 2005:C'(60) Transcribed Image Text: C(t) = 3.5 sin (%) + : +381 + ?
Answer Preview: We have Thus This means that on Decembe…

, Chapter: 3 -Problem: 6 >> For Problems use the definition of the derivative to obtain the following results.If f(x) = x4, then f'(x) = 4x3.
Answer Preview: Using the definition of the derivative we have We can …

, Chapter: 8 -Problem: 2 >> Figure 8.57 shows contours of f(x, y). List x- and y- coordinates and the value of the function at any local maximum and local minimum points, and identify which is which. Are any of these local extrema also global extrema on the region shown? If so, which ones? Transcribed Image Text: 40 35 30 25 2
Answer Preview: We can identify local extreme points on a contour diagram because these points will …

, Chapter: 6 -Problem: 33 >> (a) Between 2005 and 2015, ACME Widgets sold widgets at a continuous rate of R = R0e0.125t widgets per year, where t is time in years since January 1, 2005. Suppose they were selling widgets at a rate of 1000 per year on January 1, 2005. How many widgets did they sell between 2005 and 2015? How many did they sell if the rate on January 1, 2005 was 1,000,000 widgets per year? (b) In the first case
Answer Preview: a In the first case we are given that R 0 1000 widgets year So we …

, Chapter: 2 -Problem: 34 >> In Problems use the tangent line approximation.Given f(2) = ?4, f'(2) = ?3, approximate f(1.95).
Answer Preview: We have x 1 95 2 0 05 …

, Chapter: 1 -Problem: 24 >> The table gives the number of North American houses (millions) with analog cable TV.(a) Plot the number of houses, H, in millions, with cable TV versus year, Y.(b) Could H be a linear function of Y? Why or why not? (c) Could H be an exponential function of Y? Why or why not? Transcribed Image Text:
Answer Preview: a See Figure 1 50 b No The points in the plot do not lie even appr…

, Chapter: 3 -Problem: 58 >> With t in years since the start of 2014, worldwide annual extraction of copper is 17.9(1.025)t million tonnes. (a) How fast is the annual extraction changing at time t? Give units. (b) How fast is the annual extraction changing at the start of 2025? (c) Suppose annual extraction changes at the rate found in part (b) for the five years 2025–2030. By how much does the annual extraction change over t
Answer Preview: a Let R 17 9 1 025 t Then the annual answeion is …

, Chapter: 4 -Problem: 5 >> The cost function is C(q) = 1000 + 20q. Find the marginal cost to produce the 200th unit and the average cost of producing 200 units.
Answer Preview: The cost function is C(q) = 1000 + 20q. The margin…

, Chapter: 3 -Problem: 3 >> For Problems find the derivative. Assume that a, b, c, and k are constants.f(t) = te?2t
Answer Preview: f t 1 …

, Chapter: 3 -Problem: 26 >> Find the derivative. Assume that a, b, c, and k are constants. Transcribed Image Text: y= et 1 + ex
Answer Preview: Using the quotie…

, Chapter: 3 -Problem: 1 >> If f(x) = x2(x3 + 5), find f'(x) two ways: by using the product rule and by multiplying out before taking the derivative. Do you get the same result? Should you?
Answer Preview: By the product rule f x 2x …

, Chapter: 8 -Problem: 1 >> Concern the cost, C, of renting a car from a company which charges $40 a day and 15 cents a mile, so C = f(d, m) = 40d + 0.15m, where d is the number of days, and m is the number of miles.Make a table of values for C, using d = 1, 2, 3, 4 and m = 100, 200, 300, 400. You should have 16 values in your table.
Answer Preview: We make a table by calculating values for …

, Chapter: 3 -Problem: 30 >> Find the relative rate of change of f(t) using the formula d/dt ln f(t).f(t) = 6.8e?0.5t
Answer Preview: Since ln f t ln …

, Chapter: 1 -Problem: 19 >> A cup of coffee contains 100 mg of caffeine, which leaves the body at a continuous rate of 17% per hour. (a) Write a formula for the amount, A mg, of caffeine in the body t hours after drinking a cup of coffee. (b) Graph the function from part (a). Use the graph to estimate the half-life of caffeine. (c) Use logarithms to find the half-life of caffeine.
Answer Preview: a Since the initial amount of caffeine is 100 mg and the exponential decay rate is 0 …

, Chapter: 5 -Problem: 17 >> Use the following table to estimate ?150 f(x) dx. Transcribed Image Text: 0 3 48 X : j(x) 50 6 9 12 15 44 36 24 8
Answer Preview: Left hand sum 50 3 48 3 44…

, Chapter: 9 -Problem: 8 >> Compare the diseases modeled by each of the following differential equations with the flu model in this section. Match each set of differential equations with one of the following statements. Write a system of differential equations corresponding to each of the unmatched statements. (a) More infectious; infecteds removed more slowly.(b) More infectious; infecteds removed more quickly.(c) Less inf
Answer Preview: ANSWER I dS dt 0 04SI dI dt 0 04SI 0 21 This model is more infectious than the flu model as the tran…

, Chapter: 7 -Problem: 18 >> Which of the following functions makes the most sense as a model for the probability density representing the time (in minutes, starting from t = 0) that the next customer walks into a store? (a) p(t) = {cos t 0 ? t ? 2? et?2? t ? 2? (b) p(t) = 3e?3t for t ? 0 (c) p(t) = e?3t for t ? 0 (d) p(t) = 1?4 for 0 ? t ? 4
Answer Preview: It is not a since a probability density must be a non negative function not c sin…

, Chapter: 4 -Problem: 6 >> Let C(q) be the total cost of producing a quantity q of a certain product. See Figure 4.54.(a) What is the meaning of C(0)?(b) Describe in words how the marginal cost changes as the quantity produced increases.(c) Explain the concavity of the graph (in terms of economics).(d) Explain the economic significance (in terms of marginal cost) of the point at which the concavity changes.(e) Do you expect
Answer Preview: (a) The value of C(0) represents the fixed costs before production, that is, the cost of producing …

, Chapter: 3 -Problem: 39 >> Find the equation of the tangent line to f(x) = 10e?0.2x at x = 4.
Answer Preview: To find the equation of the line we need a point and the slope Since f 4 1…

, Chapter: 6 -Problem: 6 >> Find the integrals in Problem. Check your answers by differentiation. Transcribed Image Text: [ 2x(x² + 1)³dx
Answer Preview: We use the substi…

, Chapter: 3 -Problem: 6 >> Differentiate the functions in Problems. Assume that A and B are constants.R(q) = q2 ? 2 cos q
Answer Preview: R …

, Chapter: 8 -Problem: 2 >> A point A is shown on a contour diagram of a function f(x, y).(a) Evaluate f(A). (b) Is fx(A) positive, negative, or zero? (c) Is fy(A) positive, negative, or zero? Transcribed Image Text: y A 5- 10 -15- 20- X
Answer Preview: a The point A is on the 15 contour so f A 15 b Moving ri…

, Chapter: 6 -Problem: 32 >> Oil is leaking out of a ruptured tanker at the rate of r(t) = 50e?0.02t thousand liters per minute. (a) At what rate, in liters per minute, is oil leaking out at t = 0? At t = 60? (b) How many liters leak out during the first hour?
Answer Preview: a At time t 0 the rate of oil leakage r 0 50 thousand liter…

, Chapter: 1 -Problem: 35 >> The six graphs in Figure 1.16 show frequently observed patterns of age-specific cancer incidence rates, in number of cases per 1000 people, as a function of age. The scales on the vertical axes are equal.(a) For each of the six graphs, write a sentence explaining the effect of age on the cancer rate. (b) Which graph shows a relatively high incidence rate for children? Suggest a type of cancer that
Answer Preview: a I The incidence of cancer increase with age but the rate of increase slows down slightly The graph …

, Chapter: 1 -Problem: 32 >> The number of US households with cable television was 12,168,450 in 1977 and 73,365,880 in 2003. Estimate the average rate of change in the number of US households with cable television during this 26-year period. Give units and interpret your answer.
Answer Preview: We have During this 26 year period the number o…

, Chapter: 3 -Problem: 64 >> The time, T, in seconds for one complete oscillation of a pendulum is given by T = f(L) = 1.111 ?L, where L is the length of the pendulum in feet. Find the following quantities, with units, and interpret in terms of the pendulum. (a) f(100) (b) f'(100).
Answer Preview: a f 100 1 111100 11 11 seconds This tells us that it t…

, Chapter: 6 -Problem: 65 >> (a) Find ? (x + 5)2 dx in two ways: (i) By multiplying out (ii) By substituting w = x + 5 (b) Are the results the same? Explain.
Answer Preview: a i Multiplying out gives ii Substituting w x 5 s…

, Chapter: 4 -Problem: 12 >> The demand for a product is given by p = 90?10q. Find the elasticity of demand when p = 50. If this price rises by 2%, calculate the corresponding percentage change in demand.
Answer Preview: The elasticity of demand is given by To evaluate dqdp we solve p = 90 10q for q, …

, Chapter: 6 -Problem: 10 >> Decide whether the expression is a number or a family of functions. (Assume f(x) is a function.) Transcribed Image Text: 5+ [250 2f(x) dx
Answer Preview: Since 5 2f x dx 5 2 …

, Chapter: 6 -Problem: 4 >> Find the integrals in Problems. Transcribed Image Text: J (z+1)e²² dz
Answer Preview: Let u z 1 e 2z Thus 1 2e …

, Chapter: 8 -Problem: 10 >> Refer to Table 8.5 on page 350 giving the heat index, I, in ?F, as a function f(H, T) of the relative humidity, H, and the temperature, T , in ?F. The heat index is a temperature which tells you how hot it feels as a result of the combination of humidity and temperature. Answer the question in Problem9 for Boston in summer (H = 50, T = 80).Table 8.5 Heat index (?F)
Answer Preview: We estimate IH and IT by using difference quotients We have Choosing H 10 and reading the values fro…

, Chapter: 6 -Problem: 39 >> Find an antiderivative.g(t) = e?3t
Answer Preview: e …

, Chapter: 6 -Problem: 34 >> A graph of f is given. Let F'(x) = f(x). (a) What are the x-coordinates of the critical points of F(x)? (b) Which critical points are local maxima, which are local minima, and which are neither? (c) Sketch a possible graph of F(x). Transcribed Image Text: 2 3 + x 4 f(x)
Answer Preview: a Critical points of F x are the zeros of f …

, Chapter: 1 -Problem: 38 >> Concern the maximum heart rate (MHR), which is the maximum number of times a person’s heart can safely beat in one minute. If MHR is in beats per minute and a is age in years, the formulas used to estimate MHR areWhat can be said about the ages of a male and a female with the same maximum heart rate? Transcribed Image Text
Answer Preview: If f is the age of the female …

, Chapter: 1 -Problem: 19 >> Solve for t using natural logarithms.0 = 7 ? 3et
Answer Preview: We cannot take the log of 0 Moving the 3e t to the oth…

, Chapter: 5 -Problem: 16 >> A bicyclist accelerates at a constant rate, from 0 ft/sec to 15 ft/sec in 10 seconds. (a) Figure 5.17 shows the velocity of the bike while it is accelerating. What is the value of b in the figure? (b) How far does the bike travel while it is accelerating? Transcribed Image Text: velocity (ft/sec) b
Answer Preview: a Since the bike takes 10 second to reach its maxi…

, Chapter: 3 -Problem: 68 >> An island of A square kilometers in the Florida Keys has N species of beetles, given byN = f(A) = 8.3A0.25.(a) Find f¨(A).(b) At 40 km2, Key Largo is the largest island in the Keys. Find f(40) and f¨(40).(c) Interpret f(40) in terms of beetles and Key Largo.(d) Global warming is causing the oceans to rise, reducing land mass. Interpret f¨(40) in terms of Key Largo, shrinking land mass, and beetles
Answer Preview: a We have f A 8 3 0 25A 0 75 2 075 A 0 75 b We see that f 40 8 3 40 0 25 20 873 and …

, Chapter: 6 -Problem: 63 >> Find the exact average value of f(x) = 1?(x + 1) on the interval x = 0 to x = 2. Sketch a graph showing the function and the average value.
Answer Preview: If f x 1 x 1 the average value of f on the inter…

, Chapter: 1 -Problem: 27 >> (a) Figure 1.81 shows exponential growth. Starting at t = 0, estimate the time for the population to double.(b) Repeat part (a), but this time start at t = 3.(c) Pick any other value of t for the starting point, and notice that the doubling time is the same no matter where you start. Transcribed Image Text:
Answer Preview: (a) At t = 0, the population is 1000. The population doubles (rea…

, Chapter: 2 -Problem: 28 >> “Winning the war on poverty” has been described cynically as slowing the rate at which people are slipping below the poverty line. Assuming that this is happening: (a) Graph the total number of people in poverty against time. (b) If N is the number of people below the poverty line at time t, what are the signs of dN?dt and d2N?dt2? Explain.
Answer Preview: a Let N t be the number of people below the poverty l…

, Chapter: 5 -Problem: 21 >> After a foreign substance is introduced into the blood, the rate at which antibodies are made is given bywhere time, t, is in minutes. Assuming there are no antibodies present at time t = 0, find the total quantity of antibodies in the blood at the end of 4 minutes. Transcribed Image Text: r(t): t 1
Answer Preview: To find the total quantity of antibodies in the blood at the end of 4 minutes we ne…

, Chapter: 6 -Problem: 5 >> If G(1) = 50 and G(x) is an antiderivative of g(x) = ln x, use a calculator to find G(4).
Answer Preview: By the Fundamental Theorem the change in G x on an inte…

, Chapter: 5 -Problem: 14 >> Annual income for ages 25 to 85 is given graphically. People sometimes spend less than their income (to save for retirement) or more than their income (taking out a loan). The process of spreading out spending over a lifetime is called consumption smoothing. (a) Find the average annual income for these years. (b) Assuming that people spend at a constant rate equal to their average income, when are
Answer Preview: a Let f t be the annual income at age t Between ages 25 and 85 The integral equals the area of th…

, Chapter: 8 -Problem: 9 >> Use Lagrange multipliers to find the maximum or minimum values of f(x, y) subject to the constraint.f(x, y) = x2 + y2, 4x ? 2y = 15
Answer Preview: The objective function is f x y x 2 y 2 and the constraint equation is …

, Chapter: 5 -Problem: 43 >> The Montgolfier brothers (Joseph and Etienne) were eighteenth-century pioneers of hot-air ballooning. Had they had the appropriate instruments, they might have left us a record, like that shown in Figure 5.70, of one of their early experiments. The graph shows their vertical velocity, v, with upward as positive. (a) Over what intervals was the acceleration positive? Negative? (b) What was the grea
Answer Preview: a The acceleration is positive for 0 t 40 and for a tiny period before t 60 sinc…

, Chapter: 6 -Problem: 41 >> Consider the improper integral(a) Use a calculator or computer to find ?b1 1?(?x) dx for b = 100, 1000, 10,000. What do you notice? (b) Find ?b1 1?(?x) dx using the Fundamental Theorem of Calculus. Your answer will contain b. (c) Now take the limit as b ? ?. What does this tell you about the improper integral? Transcribed
Answer Preview: a A calculator or computer gives These …

, Chapter: 3 -Problem: 40 >> The distance, s, of a moving body from a fixed point is given as a function of time by s = 20e t?2. Find the velocity, v, of the body as a function of t.
Answer Preview: If the distance …

, Chapter: 1 -Problem: 39 >> Concern the maximum heart rate (MHR), which is the maximum number of times a person’s heart can safely beat in one minute. If MHR is in beats per minute and a is age in years, the formulas used to estimate MHR areRecently it has been suggested that a more accurate predictor of MHR for both males and females is given byMHR = 208 ? 0.7a.(a) At what age do the old and new formulas give the same MHR f
Answer Preview: a If old and new formulas give the same MHR for females we h…

, Chapter: 1 -Problem: 18 >> Simplify the quantities in Problem using m(z) = z2.m(z) ? m(z ? ?)
Answer Preview: m z …

, Chapter: 1 -Problem: 16 >> Simplify the quantities in Problem using m(z) = z2.m(z + 1) ? m(z)
Answer Preview: m z …

, Chapter: 4 -Problem: 3 >> Indicate all critical points of the function f. How many critical points are there? Identify each critical point as a local maximum, a local minimum, or neither. Transcribed Image Text: f(t) t
Answer Preview: We find a critical point by noting where f t 0 or f is undefined Since the curve is smooth through…

, Chapter: 6 -Problem: 57 >> Use integration by substitution and the Fundamental Theorem to evaluate the definite integrals in Problems. Transcribed Image Text: [² 0 x (1 + x²)² dx
Answer Preview: We substitu…

, Chapter: 4 -Problem: 10 >> Figure 4.99 shows the plasma levels of canrenone in a healthy volunteer after a single oral dose of spironolactone given on a fasting stomach and together with a standardized breakfast. Discuss the effect of food on peak concentration and time to reach peak concentration. Is the effect of the food strongest during the first 8 hours, or after 8 hours?
Answer Preview: From the graph in Figure 4 99, we can see that the peak concentration of canrenone is higher when it …

, Chapter: 3 -Problem: 41 >> Let f(t) = t2 ? 4t + 5. (a) Find f'(t). (b) Find f'(1) and f'(2). (c) Use a graph of f(t) to check that your answers to part (b) are reasonable. Explain.
Answer Preview: a f t 2t 4 b f 1 2 1 4 2 f 2 2 2 4 0 c We see from part b that f 2 0 This means that the sl…

, Chapter: 6 -Problem: 2 >> Explain how you can tell if substitution can be used to find an antiderivative. Transcribed Image Text: x(1 - 5x²)5 dx
Answer Preview: Setting 1 5x 2 we see that d 10x dx Since the integ…

, Chapter: 5 -Problem: 1 >> Find the area under the graph of f(x) = x2 +2 between x = 0 and x = 6.
Answer Preview: Since f x is posi…

, Chapter: 8 -Problem: 12 >> A topographic map is given in Figure 8.30. How many hills are there? Estimate the x- and y-coordinates of the tops of the hills. Which hill is the highest? A river runs through the valley; in which direction is it flowing? Transcribed Image Text: y 8 7 6 5 4 3 2 in 43 210 224 in 1 2 3 4 5 6 7 8 Figu
Answer Preview: To find the hills we look for areas of the map with concentric contour arcs that increase a…

, Chapter: 6 -Problem: 39 >> Problems concern the graph of f' in Figure 6.21.Which is greater, f(0) or f(1)? Transcribed Image Text: y 2 3 X y = f'(x) Figure 6.21: Note: Graph of f', not f
Answer Preview: By the Fundamental Theor…

, Chapter: 3 -Problem: 16 >> Differentiate the functions in Problems. Assume that A and B are constants.f(x) = x2 cos x
Answer Preview: f x 2x c…

, Chapter: 2 -Problem: 39 >> Problems concern g(t) in Figure 2.35, which gives the weight of a human fetus as a function of its age.(a) What are the units of g¨(24)? (b) What is the biological meaning of g¨(24) = 0.096? Transcribed Image Text: weight (kg) 3 2 1 8 16 24 g(1) 1, age of fetus 40 (weeks after last menstruation) 32
Answer Preview: a kilograms per week b At we…

, Chapter: 1 -Problem: 27 >> Write the functions in Problems  in the form P = P0at. Which represent exponential growth and which represent exponential decay?P = P0e0.2t
Answer Preview: P P 0 e 0 2 t …

, Chapter: 1 -Problem: 30 >> The gas mileage of a car (in miles per gallon) is highest when the car is going about 45 miles per hour and is lower when the car is going faster or slower than 45 mph. Graph gas mileage as a function of speed of the car.
Answer Preview: Figure 1 9 shows one possible graph …

, Chapter: 1 -Problem: 19 >> Find a possible formula for the graph. Transcribed Image Text: 5 y + x ??
Answer Preview: This graph is a co…

, Chapter: 4 -Problem: 2 >> The elasticity of a good is E = 2. What is the effect on the quantity demanded of:(a) A 3% price increase?(b) A 3% price decrease?
Answer Preview: The effect on the quantity demanded is approximately E tim…

, Chapter: 6 -Problem: 56 >> Use integration by substitution and the Fundamental Theorem to evaluate the definite integrals in Problems. Transcribed Image Text: e-2 1 [²²= -dt -1 1+2
Answer Preview: We substitute w …

, Chapter: 4 -Problem: 5 >> Problem are about chikungunya, a disease that arrived in the Americas in 2013 and spread rapidly in 2014. While seldom fatal, the disease causes debilitating joint pain and a high fever. In August 2014, a public challenge was issued to predict the number of cases in each of the affected countries. The winners, Joceline Lega and Heidi Brown, used a logistic model to make their predictions. Let N be
Answer Preview: The logistic curve levels off at the value L in the formula Thus, the country …

, Chapter: 2 -Problem: 49 >> Figure 2.37 shows how the pumping rate of a person’s heart changes after bleeding. (a) Find the slope of the line tangent to the graph at time 2 hours. Give units. (b) Using your answer to part (a), estimate how much the pumping rate increases during the minute beginning at time 2 hours. (c) Express your answer to part (a) as a derivative of g(t).
Answer Preview: a The slope of the …

, Chapter: 3 -Problem: 1 >> Differentiate the functions in Problem. Assume that A and B are constants.P = 3 + cos t
Answer Preview: dP…

, Chapter: 6 -Problem: 4 >> Decide if the function is an antiderivative of f(x) = 2e2x.F(x) = xe2x
Answer Preview: Since F x e 2x …

, Chapter: 5 -Problem: 2 >> Rectangles have been drawn to approximate ?60 g(x) dx. (a) Do the rectangles represent a left or a right sum? (b) Do the rectangles lead to an upper or a lower estimate? (c) What is the value of n? (d) What is the value of ?x? Transcribed Image Text: g(x) 6 X
Answer Preview: a Left …

, Chapter: 8 -Problem: 9 >> Figure 8.27 shows the contours of the temperature H in a room near a recently opened window. Label the three contours with reasonable values of H if the house is in the following locations. (a) Minnesota in winter (where winters are harsh). (b) San Francisco in winter (where winters are mild). (c) Houston in summer (where summers are hot). (d) Oregon in summer (where summers are mild).
Answer Preview: Many different answers are possible Answers are in …

, Chapter: 8 -Problem: 14 >> Table 8.7 gives the number of calories burned per minute, B = f(s,w), for someone roller-blading, as a function of the person’s weight, w, and speed, s. (a) Is fw positive or negative? Is fs positive or negative? What do your answers tell us about the effect of weight and speed on calories burned per minute? (b) Estimate fw(160, 10) and fs(160, 10). Interpret your answers.
Answer Preview: a We see that f w is positive since B increases as w increases when s is held …

, Chapter: 3 -Problem: 37 >> Find the equation of the tangent line to the graph of f(x) = x3ex at the point at which x = 2.
Answer Preview: Since f 2 2 3 e 2 59 112 the tangent line passes through the point 2 59 11…

,

, Chapter: 1 -Problem: 26 >> The number of people living with HIV increased worldwide approximately exponentially from 2.5 million in 1985 to 36.7 million in 2015. (HIV is the virus that causes AIDS.)(a) Give a formula for the number of people living with HIV, H (in millions), as a function of years, t, since 1985. Use the form H = H0ekt. Graph this function. (b) What was the yearly continuous percent change in the number of
Answer Preview: a We use an exponential function in the form H H 0 e kt Since t is in years since 1985 the initi…

, Chapter: 1 -Problem: 15 >> Write a formula representing the function.The average velocity, v, for a trip over a fixed distance, d, is inversely proportional to the time of travel, t.
Answer Preview: If di…

, Chapter: 1 -Problem: 17 >> The function S = f(t) gives the average annual sea level, S, in meters, in Aberdeen, Scotland,7 as a function of t, the number of years before 2012. Write a mathematical expression that represents the given statement.In 2000 the average annual sea level in Aberdeen was 7.049 meters.
Answer Preview: The year 2000 was 12 year…

, Chapter: 3 -Problem: 67 >> Circulation time is the average amount of time it takes for all the blood in the body to circulate once and return to the heart. For a mammal with mass m kilograms, the circulation time C, in seconds, isC = f(m) = 17.4m0.25.(a) Find f¨(m). (b) For a human with mass 70 kg, find and interpret f(70) and f¨(70).
Answer Preview: a We have f m 17 4 0 25m 0 75 4 35 m 0 75 b We see that f 70 1…

, Chapter: 7 -Problem: 15 >> Graph a possible density function representing crop yield (in kilograms) from a field under the given circumstance.All yields from 0 to 100 kg are equally likely; the field never yields more than 100 kg.
Answer Preview: If x is the yield in kg th…

, Chapter: 4 -Problem: 13 >> School organizations raise money by selling candy door to door. The table shows p, the price of the candy, and q, the quantity sold at that price. (a) Estimate the elasticity of demand at a price of $1.00. At this price, is the demand elastic or in- elastic?(b) Estimate the elasticity at each of the prices shown. What do you notice? Give an explanation for why this might be so.(c) At approximately
Answer Preview: (a) We use So we approximate dqdp at p = 1 00. Since E = 0 470 (b…

, Chapter: 2 -Problem: 27 >> Values of x and g(x) are given in the table. For what value of x does g'(x) appear to be closest to 3? Transcribed Image Text: 6.2 2.7 3.2 3.7 4.2 4.7 5.2 5.7 g(x) 3.4 4.4 5.0 5.4 6.0 7.4 9.0 11.0 x
Answer Preview: The value of g x is increasing at a de…

, Chapter: 4 -Problem: 14 >> In Problems graph the function and describe in words the interesting features of the graph, including the location of the critical points and where the function is monotonic (that is, increasing or decreasing). Then use the derivative and algebra to explain the shape of the graph.f(x) = x3 + 6x + 1
Answer Preview: The graph of f in Figure 4 13 appears to be …

, Chapter: 3 -Problem: 22 >> Find the derivative. Assume a, b, c, k are constants. Transcribed Image Text: h(0) = 1 ' ?
Answer Preview: Since h …

, Chapter: 8 -Problem: 11 >> Refer to Table 8.3, which shows the weekly beef consumption, C, (in lbs) of an average household as a function of p, the price of beef (in $/lb) and I, annual household income (in $1000s).Make a table of the proportion, P, of household income spent on beef per week as a function of price and income. Transcribed Image Text:
Answer Preview: Table 8 8 gives the amount M spent on beef per household per week Thus the …

, Chapter: 8 -Problem: 16 >> Using Table 8.4, graph heat index as a function of humidity with temperature fixed at 70?F and at 100?F. Explain the features of each graph and the difference between them in common-sense terms. Transcribed Image Text: Table 8.4 Heat index (°F) as a function of humidity (H%) and temperature (°F) H 7
Answer Preview: Both graphs are increasing because at any fixed temperature the air feels hotter as t…

, Chapter: 6 -Problem: 29 >> Find the integrals in Problem. Check your answers by differentiation. Transcribed Image Text: t 1+ 3t² dt
Answer Preview: We use the substitution w 1 3t 2 d…

, Chapter: 2 -Problem: 45 >> US beef production, M = f(t), in billion pounds, is a function of t, years since 2010. (a) Interpret f(5) = 23.7 and f'(5) = ?0.1 in terms of beef production. (b) Estimate f(8) and interpret it in terms of beef production.
Answer Preview: a The statement f 5 23 7 tells us that beef production was 23 7 billion pounds in 2015 Th…

, Chapter: 1 -Problem: 42 >> Concern biodiesel, a fuel derived from renewable resources such as food crops, algae, and animal oils. The table shows the percent growth over the previous year in US biodiesel consumption.(a) True or false: The annual US consumption of biodiesel grew exponentially from 2008 to 2010. Justify your answer without doing any calculations.(b) According to this data, during what single year(s), if any,
Answer Preview: a False because the annual percent gr…

, Chapter: 1 -Problem: 30 >> When the price, p, charged for a boat tour was $25, the average number of passengers per week, N, was 500. When the price was reduced to $20, the average number of passengers per week increased to 650. Find a formula for the demand curve, assuming that it is linear.
Answer Preview: We know that a formula for passengers versus price will take the form N mp b where …

, Chapter: 5 -Problem: 20 >> A bungee jumper leaps off the starting platform at time t = 0 and rebounds once during the first 5 seconds. With velocity measured downward, for t in seconds and 0 ? t ? 5, the jumper’s velocity is approximated by v(t) = ?4t2 + 16t meters/sec. (a) How many meters does the jumper travel during the first five seconds? (b) Where is the jumper relative to the starting position at the end of the five s
Answer Preview: a Solving v t 4t 2 16t 0 gives t 0 and t 4 At t 0 the jump has just started at t 4 the jumper is …

, Chapter: 1 -Problem: 21 >> The functions in Problems represent exponential growth or decay. What is the initial quantity? What is the growth rate? State if the growth rate is continuous.P = 5(1.07)t
Answer Preview: Initial …

, Chapter: 4 -Problem: 1 >> For each cost function in Figure 4.64, is there a value of q at which average cost is minimized? If so, approximately where? Explain your answer.(a)(b) Transcribed Image Text: (cost) ? q (quantity)
Answer Preview: a Since the graph is concave down the average cost gets smaller as q …

, Chapter: 7 -Problem: 12 >> The cumulative distribution function for heights (in meters) of trees in a forest is F(x). (a) Explain in terms of trees the meaning of the statement F(7) = 0.6. (b) Which is greater, F(6) or F(7)? Justify your answer in terms of trees.
Answer Preview: a F 7 0 6 tells us that 60 of the trees in the fo…

, Chapter: 4 -Problem: 9 >> Shows how a surge can be modeled with a difference of exponential decay functions. (a) Using graphs of e?t and e?2t, explain why the graph of f(t) = e?t ? e?2t has the shape of a surge. (b) Find the critical point and inflection point of f.
Answer Preview: (a) The value f(t) = e t e 2t is the vertical distance between the two cu…

, Chapter: 4 -Problem: 15 >> The demand for yams is given in Problem 14. (a) At a price of $2 per pound, what is the total revenue for the yam farmer? (b) Write revenue as a function of price, and then find the price that maximizes revenue. (c) What quantity is sold at the price you found in part (b), and what is the total revenue? (d) Show that E = 1 at the price you found in part (b).
Answer Preview: a At a price of 2 pound the quantity sold is q 5000 10 2 2 5000 40 4960 so the total revenue is R pq …

, Chapter: 6 -Problem: 6 >> Decide if the function is an antiderivative of f(x) = 2e2x. Transcribed Image Text: + S' F(x) = ²x + e²¹ dt
Answer Preview: Since the definite integral in the …

, Chapter: 2 -Problem: 22 >> For the function f(x) = 3x, estimate f'(1). From the graph of f(x), would you expect your estimate to be greater than or less than the true value of f'(1)?
Answer Preview: Using the interval 1 x 1 001 we e…

, Chapter: 8 -Problem: 14 >> The quantity, Q, of a certain product manufactured depends on the quantity of labor, L, and of capital, K, used according to the functionQ = 900L1?2K2?3.Labor costs $100 per unit and capital costs $200 per unit. What combination of labor and capital should be used to produce 36,000 units of the goods at minimum cost? What is that minimum cost?
Answer Preview: We want to minimize cost C 100L 200K subject to Q 900L 12 …

, Chapter: 6 -Problem: 31 >> Find an antiderivative.f(x) = 5x ? ?x
Answer Preview: 5 I…

, Chapter: 2 -Problem: 39 >> Use the definition of the derivative to show how the formulas in Problem are obtained.If f(x) = 5x2 + 1, then f¨(x) = 10x.
Answer Preview: Using the definition of the derivative we have As gets very …

, Chapter: 1 -Problem: 28 >> Figure 1.43 shows the length, L, in cm, of a sturgeon (a type of fish) as a function of the time, t, in years.(a) Is the function increasing or decreasing? Is the graph concave up or concave down? (b) Estimate the average rate of growth of the sturgeon between t = 5 and t = 15. Give units and interpret your answer in terms of the sturgeon.
Answer Preview: a This function is increasing and the graph is concave down b …

, Chapter: 8 -Problem: 20 >> Find all the critical points and determine whether each is a local maximum, local minimum, a saddle point, or none of these.f(x, y) = x3 + y3 ? 6y2 ? 3x + 9
Answer Preview: To find the critical points we solve f x 0 and f y 0 …

, Chapter: 9 -Problem: 17 >> The amount of land in use for growing crops increases as the world’s population increases. Suppose A(t) represents the total number of hectares of land in use in year t. (A hectare is about 2 1/2 acres.) (a) Explain why it is plausible that A(t) satisfies the equation A'(t) = kA(t).What assumptions are you making about the world’s population and its relation to the amount of land used? (b) In 1966
Answer Preview: a Assuming that the worlds population grows exponentially satisfy…

, Chapter: 4 -Problem: 2 >> Figure 4.65 shows cost with q = 10,000 marked. (a) Find the average cost when the production level is 10,000 units and interpret it. (b) Represent your answer to part (a) graphically. (c) At approximately what production level is average cost minimized? Transcribed Image Text: 20,000 10,000 A XXX 10
Answer Preview: a The average cost of quantity q is given by the formula C q q From the graph we see that C 10 000 1…

, Chapter: 7 -Problem: 4 >> In an agricultural experiment, the quantity of grain from a given size field is measured. The yield can be anything from 0 kg to 50 kg. For each of the following situations, pick the graph that best represents the: (i) Probability density function (ii) Cumulative distribution function. (a) Low yields are more likely than high yields. (b) All yields are equally likely. (c) High yields are more like
Answer Preview: a i The probability density function is III ii The cu…

, Chapter: 4 -Problem: 8 >> Table 4.2 shows cost, C(q), and revenue, R(q). (a) At approximately what production level, q, is profit maximized? Explain your reasoning.(b) What is the price of the product?(c) What are the fixed costs? Transcribed Image Text: Table 4.2 0 500 1000 1500 2000 2500 3000 0 1500 3000 4500 6000 7500 90
Answer Preview: (a) Profit is maximized when R(q) C(q) is as lar…

, Chapter: 6 -Problem: 10 >> Supply and demand curves for a product are in Figure 6.41. (a) Estimate the equilibrium price and quantity. (b) Estimate the consumer and producer surplus. Shade them. (c) What are the total gains from trade for this product? Transcribed Image Text: p ($/unit) 100 80 60 40 20 50 100 150 200 250 Figu
Answer Preview: a Looking at the figure in the problem we see that the equilibrium price is roughly 30 giving a…

, Chapter: 3 -Problem: 26 >> Find the derivative. Assume a, b, c, k are constants. Transcribed Image Text: 7 y = 315-5?t +- t
Answer Preview: y …

, Chapter: 2 -Problem: 24 >> Match f' with the corresponding f in Figure 2.30. Transcribed Image Text: (1) € + (V) 3 1 + x € (IV) -1 X + -1 1 Figure 2.30 X + x 1 X
Answer Preview: Since f x 0 for all x we know that f is i…

, Chapter: 6 -Problem: 32 >> Figure 6.19 shows the derivative F'(t). If F(0) = 3, find the values of F(2), F(5), F(6). Graph F(t). Transcribed Image Text: Area = 5 2 F' (t) 5 Area = 16 Figure 6.19 6 t Area = 10
Answer Preview: The areas given enable us to calculate the changes in the fu…

, Chapter: 2 -Problem: 34 >> In 2009, a study was done on the impact of sea-level rise in the mid-Atlantic states. Let a(t) be the depth of the sea in millimeters (mm) at a typical point on the Atlantic Coast, and let m(t) be the depth of the sea in mm at a typical point on the Gulf of Mexico, with time t in years since data collection started. (a) The study reports “Sea level is rising and there is evidence that the rate is
Answer Preview: a Since the sea level is rising we know that a t 0 and m t 0 Si…

, Chapter: 1 -Problem: 40 >> Ask you to plot graphs based on the following story: “As I drove down the highway this morning, at first traffic was fast and uncongested, then it crept nearly bumper to-bumper until we passed an accident, after which traffic flow went back to normal until I exited.”Distance between cars vs distance driven on the highway
Answer Preview: See Figure …

, Chapter: 1 -Problem: 19 >> Use Figure 1.25 showing how the quantity, Q, of grass (kg/hectare) in different parts of Namibia depended on the average annual rainfall, r, (mm), in two different years.Figure 1.25(a) For 1939, find the slope of the line, including units. (b) Interpret the slope in this context. (c) Find the equation of the line. Transcri
Answer Preview: a Reading coordinates from the graph we see that ra…

, Chapter: 5 -Problem: 20 >> Use the following table to estimate the area between f(x) and the x-axis on the interval 0 ? x ? 20. Transcribed Image Text: x 0 5 10 15 20 f(x) 15 18 20 16 12
Answer Preview: It appears that f x is positive on the whole interval 0 x …

, Chapter: 1 -Problem: 20 >> Solve for t using natural logarithms.Pe4t ? Qe?t = 0
Answer Preview: Since we cannot take the log of 0 we move Qe 4 to the other s…

, Chapter: 4 -Problem: 12 >> Use the first derivative to find all critical points and use the second derivative to find all inflection points. Use a graph to identify each critical point as a local maximum, a local minimum, or neither.f(x) = x2 ? 5x + 3
Answer Preview: ANSWER First let s find the first derivative of f x f x 2x 5 …

, Chapter: 4 -Problem: 13 >> (a) Find the average cost at each of the production levels q in the table.(b) At which q-value shown does the average cost have a critical point?(c) Is the critical value a local maximum, local minimum, or neither? Transcribed Image Text:

Additional Information

10 Reviews for Applied Calculus Textbook Questions And Answers