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7th Edition

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Publisher: Cengage Learning,

ISBN: 9781337291248

Chapter 3.5, Problem 41E

Textbook Problem

In Exercises 41-48, estimate the indicated derivative by any method. [**HINT:** See Example 2.]

Applied Calculus

Ch. 3.1 - In Exercises 14, use the given table of values to...Ch. 3.1 - In Exercises 14, use the given table of values to...Ch. 3.1 - In Exercises 14, use the given table of values to...Ch. 3.1 - In Exercises 14, use the given table of values to...Ch. 3.1 - In Exercises 534, estimate the given limit...Ch. 3.1 - In Exercises 534, estimate the given limit...Ch. 3.1 - In Exercises 534, estimate the given limit...Ch. 3.1 - In Exercises 534, estimate the given limit...Ch. 3.1 - In Exercises 534, estimate the given limit...Ch. 3.1 - In Exercises 534, estimate the given limit...

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Acquisition of Language The percentage p(t)...Ch. 3.3 - Acquisition of Language The percentage q(t)...Ch. 3.3 - Describe the algebraic method of evaluating limits...Ch. 3.3 - What is a closed-form function? What can we say...Ch. 3.3 - Your friends Rita and Richard are arguing. Rita...Ch. 3.3 - Your other friends, Andrew and Dorothy, are also...Ch. 3.3 - Why was the following marked wrong? What is the...Ch. 3.3 - Why was the following marked wrong? What is the...Ch. 3.3 - Your friend Karin tells you that f(x)=1/(x2)2...Ch. 3.3 - Give an example of a function f specified by means...Ch. 3.3 - Give examples of two limits that lead to two...Ch. 3.3 - Give examples of two limits: one that leads to a...Ch. 3.3 - (Compare Exercise 73 in Section 3.1.) Which...Ch. 3.3 - (Compare Exercise 74 in Section 3.1.) Which in...Ch. 3.3 - What is wrong with the following statement? If...Ch. 3.3 - What is wrong with the following statement? If...Ch. 3.3 - Give the formula for a function that is continuous...Ch. 3.3 - Give the formula for a function that is continuous...Ch. 3.3 - The Indeterminate Form An indeterminate form not...Ch. 3.3 - The Indeterminate Form 1 An indeterminate form not...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 118, calculate the average rate of...Ch. 3.4 - In Exercises 1924, calculate the average rate of...Ch. 3.4 - In Exercises 1924, calculate the average rate of...Ch. 3.4 - In Exercises 1924, calculate the average rate of...Ch. 3.4 - In Exercises 1924, calculate the average rate of...Ch. 3.4 - In Exercises 1924, calculate the average rate of...Ch. 3.4 - In Exercises 1924, calculate the average rate of...Ch. 3.4 - World Military Expenditure The following table...Ch. 3.4 - Education Expenditure The following table shows...Ch. 3.4 - Crude Oil Production: Mexico The following table...Ch. 3.4 - Offshore Crude Oil Production: Mexico The...Ch. 3.4 - Subprime Mortgages during the Housing Crisis The...Ch. 3.4 - Subprime Mortgage Debt during the Housing Crisis...Ch. 3.4 - Immigration to Ireland The following graph shows...Ch. 3.4 - Emigration from Ireland The following graph shows...Ch. 3.4 - Science Research in the United States The...Ch. 3.4 - Science Research in Europe The following table...Ch. 3.4 - College Basketball: Men The following chart shows...Ch. 3.4 - College Basketball: Women The following chart...Ch. 3.4 - Funding for the Arts State governments in the...Ch. 3.4 - Funding for the Arts The U.S. federal government...Ch. 3.4 - Market Index Joe Downs runs a small investment...Ch. 3.4 - Market Index Refer to the Joe Downs Index in...Ch. 3.4 - Crude Oil Prices The price per barrel of crude oil...Ch. 3.4 - Median Home Prices The median home price in the...Ch. 3.4 - End of the Earth In 5 billion year the Sun will...Ch. 3.4 - End of the Earth In 5 billion year the Sun will...Ch. 3.4 - The 2003 SARS Outbreak In the early stages of the...Ch. 3.4 - The 2003 SARS Outbreak A few weeks into the SARS...Ch. 3.4 - The 2014 Ebola Outbreak In the first 6 months of...Ch. 3.4 - The 2014 Ebola Outbreak Repeat Exercise 49 using...Ch. 3.4 - Ecology Increasing numbers of manatees (sea...Ch. 3.4 - Ecology Refer to Exercises 51. a. Compute the...Ch. 3.4 - SAT Scores by Income The math SAT score of a high...Ch. 3.4 - SAT Scores by Income Repeat Exercise 53 using the...Ch. 3.4 - Describe three ways we have used to determine the...Ch. 3.4 - If f is a linear function of x with slope m, what...Ch. 3.4 - Is the average rate of change of a function over...Ch. 3.4 - If the average rate of change of a function over...Ch. 3.4 - Sketch the graph of a function whose average rate...Ch. 3.4 - Sketch the graph of a function whose average rate...Ch. 3.4 - If the rate of change of quantity A is 2 units of...Ch. 3.4 - If the rate of change of quantity A is 2 units of...Ch. 3.4 - A certain function f has the property that its...Ch. 3.4 - A certain function f has the property that its...Ch. 3.4 - Is it possible for a companys revenue to have a...Ch. 3.4 - Is it possible for a companys revenue to have a...Ch. 3.4 - The average rate of change of f over [1,3] is (A)...Ch. 3.4 - The average rate of change of f over [1,4] is (A)...Ch. 3.5 - In Exercises 14, estimate the derivative from the...Ch. 3.5 - In Exercises 14, estimate the derivative from the...Ch. 3.5 - In Exercises 14, estimate the derivative from the...Ch. 3.5 - In Exercises 14, estimate the derivative from the...Ch. 3.5 - Consider the functions in Exercises 58 as...Ch. 3.5 - Consider the functions in Exercises 58 as...Ch. 3.5 - Consider the functions in Exercises 58 as...Ch. 3.5 - Consider the functions in Exercises 58 as...Ch. 3.5 - In Exercises 912 the function gives the cost to...Ch. 3.5 - In Exercises 912 the function gives the cost to...Ch. 3.5 - In Exercises 912 the function gives the cost to...Ch. 3.5 - In Exercises 912 the function gives the cost to...Ch. 3.5 - In Exercises 1316 the graph of a function is shown...Ch. 3.5 - In Exercises 1316 the graph of a function is shown...Ch. 3.5 - In Exercises 1316 the graph of a function is shown...Ch. 3.5 - In Exercises 1316 the graph of a function is shown...Ch. 3.5 - In Exercises 1722, say at which labeled point the...Ch. 3.5 - In Exercises 1722, say at which labeled point the...Ch. 3.5 - In Exercises 1722, say at which labeled point the...Ch. 3.5 - In Exercises 1722, say at which labeled point the...Ch. 3.5 - In Exercises 1722, say at which labeled point the...Ch. 3.5 - In Exercises 1722, say at which labeled point the...Ch. 3.5 - In each of Exercises 2326, three slopes are given....Ch. 3.5 - In each of Exercises 2326, three slopes are given....Ch. 3.5 - In each of Exercises 2326, three slopes are given....Ch. 3.5 - In each of Exercises 2326, three slopes are given....Ch. 3.5 - In Exercises 2730, find the approximate...Ch. 3.5 - In Exercises 2730, find the approximate...Ch. 3.5 - In Exercises 2730, find the approximate...Ch. 3.5 - In Exercises 2730, find the approximate...Ch. 3.5 - Complete the following: The tangent to the graph...Ch. 3.5 - Complete the following: The difference quotient...Ch. 3.5 - Which is correct? The derivative function assigns...Ch. 3.5 - Which is correct? The derivative function f(x)...Ch. 3.5 - Let f have the graph shown. a. The average rate of...Ch. 3.5 - A function f has the following graph. a. The...Ch. 3.5 - In Exercises 3740, use a quick approximation to...Ch. 3.5 - In Exercises 3740, use a quick approximation to...Ch. 3.5 - In Exercises 3740, use a quick approximation to...Ch. 3.5 - In Exercises 3740, use a quick approximation to...Ch. 3.5 - In Exercises 41-48, estimate the indicated...Ch. 3.5 - In Exercises 41-48, estimate the indicated...Ch. 3.5 - In Exercises 41-48, estimate the indicated...Ch. 3.5 - In Exercises 41-48, estimate the indicated...Ch. 3.5 - In Exercises 41-48, estimate the indicated...Ch. 3.5 - In Exercises 41-48, estimate the indicated...Ch. 3.5 - In Exercises 41-48, estimate the indicated...Ch. 3.5 - In Exercises 41-48, estimate the indicated...Ch. 3.5 - In Exercises 4954, (a) use any method to estimate...Ch. 3.5 - In Exercises 4954, (a) use any method to estimate...Ch. 3.5 - In Exercises 4954, (a) use any method to estimate...Ch. 3.5 - In Exercises 4954, (a) use any method to estimate...Ch. 3.5 - In Exercises 4954, (a) use any method to estimate...Ch. 3.5 - In Exercises 4954, (a) use any method to estimate...Ch. 3.5 - In Exercises 55-58, estimate the given quantity....Ch. 3.5 - In Exercises 55-58, estimate the given quantity....Ch. 3.5 - In Exercises 55-58, estimate the given quantity....Ch. 3.5 - In Exercises 55-58, estimate the given quantity....Ch. 3.5 - In Exercises 5964, match the graph of f to the...Ch. 3.5 - In Exercises 5964, match the graph of f to the...Ch. 3.5 - In Exercises 5964, match the graph of f to the...Ch. 3.5 - In Exercises 5964, match the graph of f to the...Ch. 3.5 - In Exercises 5964, match the graph of f to the...Ch. 3.5 - In Exercises 5964, match the graph of f to the...Ch. 3.5 - In Exercises 6568 the graph of a function is...Ch. 3.5 - In Exercises 6568 the graph of a function is...Ch. 3.5 - In Exercises 6568 the graph of a function is...Ch. 3.5 - In Exercises 6568 the graph of a function is...Ch. 3.5 - In Exercises 6972 the graph of the derivative of a...Ch. 3.5 - In Exercises 6972 the graph of the derivative of a...Ch. 3.5 - In Exercises 6972 the graph of the derivative of a...Ch. 3.5 - In Exercises 6972 the graph of the derivative of a...Ch. 3.5 - In Exercises 73 and 74, use technology to graph...Ch. 3.5 - In Exercises 73 and 74, use technology to graph...Ch. 3.5 - In Exercises 75 and 76, use the method of Example...Ch. 3.5 - In Exercises 75 and 76, use the method of Example...Ch. 3.5 - Temperatures on Mars The air temperature one...Ch. 3.5 - Temperatures on Venus The air temperature one...Ch. 3.5 - Demand Suppose the demand for a new brand of...Ch. 3.5 - Demand Suppose the demand for an old brand of TV...Ch. 3.5 - Oil Imports from Mexico The following graph shows...Ch. 3.5 - Oil Production in Mexico The following graph shows...Ch. 3.5 - Prison Population The following curve is a model...Ch. 3.5 - Demand for Freon 12 The demand for...Ch. 3.5 - Velocity If a stone is dropped from a height of...Ch. 3.5 - Velocity If a stone is thrown down at 120 ft/s...Ch. 3.5 - Crude Oil Prices The price per barrel of crude oil...Ch. 3.5 - Median Home Prices The median home price in the...Ch. 3.5 - The 2003 SARS Outbreak In the early stages of the...Ch. 3.5 - The 2003 SARS Outbreak A few weeks into the SARS...Ch. 3.5 - The 2014 Ebola Outbreak In the first 6 months of...Ch. 3.5 - The 2014 Ebola Outbreak In the first 6 months of...Ch. 3.5 - Early Internet Services On January 1, 1996,...Ch. 3.5 - Early Internet Services On January 1, 1996,...Ch. 3.5 - Learning to Speak Let p(t) represent the...Ch. 3.5 - Learning to Read Let p(t) represent the percentage...Ch. 3.5 - Subprime Mortgages during the Housing Crisis (Com-...Ch. 3.5 - Subprime Mortgages during the Housing Crisis (Com-...Ch. 3.5 - Embryo Development The oxygen consumption of a...Ch. 3.5 - Embryo Development The oxygen consumption of a...Ch. 3.5 - The next two exercises are applications of...Ch. 3.5 - The next two exercises are applications of...Ch. 3.5 - In which, if any, of the following cases is f...Ch. 3.5 - In which, if any, of the following cases is f...Ch. 3.5 - Explain why we cannot put h=0 in the approximation...Ch. 3.5 - The balanced difference quotient...Ch. 3.5 - Let H(t) represent the number of Handbook members...Ch. 3.5 - Let F(t) represent the net earnings of Footbook,...Ch. 3.5 - It is now 8 months since the Garden City lacrosse...Ch. 3.5 - Having been soundly defeated in the national...Ch. 3.5 - Company As profits are given by P(0)=1 millionand...Ch. 3.5 - Company Cs profits are given by P(0)=1 millionand...Ch. 3.5 - During the 1-month period starting last January 1,...Ch. 3.5 - During the 1-month period starting last January 1,...Ch. 3.5 - If the derivative of f is zero at a point, what do...Ch. 3.5 - Sketch the graph of a function whose derivative...Ch. 3.5 - Sketch the graph of a function whose derivative...Ch. 3.5 - Sketch the graph of a function whose derivative is...Ch. 3.5 - Use the difference quotient to explain the fact...Ch. 3.5 - Give a numerical explanation of the fact that if f...Ch. 3.5 - Consider the following values of the function f...Ch. 3.5 - Consider the following values of the function g...Ch. 3.5 - Sketch the graph of a function whose derivative is...Ch. 3.5 - Sketch the graph of a function whose derivative is...Ch. 3.5 - Here is the graph of the derivative f ofa function...Ch. 3.5 - Here is the graph of the derivative f ofa function...Ch. 3.5 - Professor Talker of the physics department drove a...Ch. 3.5 - Professor Silent, another physics professor, drove...Ch. 3.5 - Draw the graph of a function f with the property...Ch. 3.5 - Draw the graph of a function f with the property...Ch. 3.6 - In Exercises 1-14, compute f(a) algebraically for...Ch. 3.6 - In Exercises 1-14, compute f(a) algebraically for...Ch. 3.6 - In Exercises 1-14, compute f(a) algebraically for...Ch. 3.6 - In Exercises 1-14, compute f(a) algebraically for...Ch. 3.6 - In Exercises 1-14, compute f(a) algebraically for...Ch. 3.6 - In Exercises 1-14, compute f(a) algebraically for...Ch. 3.6 - In Exercises 1-14, compute f(a) algebraically for...Ch. 3.6 - In Exercises 1-14, compute f(a) algebraically for...Ch. 3.6 - In Exercises 1-14, compute f(a) algebraically for...Ch. 3.6 - In Exercises 1-14, compute f(a) algebraically for...Ch. 3.6 - In Exercises 1-14, compute f(a) algebraically for...Ch. 3.6 - In Exercises 1-14, compute f(a) algebraically for...Ch. 3.6 - In Exercises 1-14, compute f(a) algebraically for...Ch. 3.6 - In Exercises 1-14, compute f(a) algebraically for...Ch. 3.6 - In Exercises 15-28, compute the derivative...Ch. 3.6 - In Exercises 15-28, compute the derivative...Ch. 3.6 - In Exercises 15-28, compute the derivative...Ch. 3.6 - In Exercises 15-28, compute the derivative...Ch. 3.6 - In Exercises 15-28, compute the derivative...Ch. 3.6 - In Exercises 15-28, compute the derivative...Ch. 3.6 - In Exercises 15-28, compute the derivative...Ch. 3.6 - In Exercises 15-28, compute the derivative...Ch. 3.6 - In Exercises 15-28, compute the derivative...Ch. 3.6 - In Exercises 15-28, compute the derivative...Ch. 3.6 - In Exercises 15-28, compute the derivative...Ch. 3.6 - In Exercises 15-28, compute the derivative...Ch. 3.6 - In Exercises 15-28, compute the derivative...Ch. 3.6 - In Exercises 15-28, compute the derivative...Ch. 3.6 - In Exercises 29-38, compute the indicated...Ch. 3.6 - In Exercises 29-38, compute the indicated...Ch. 3.6 - In Exercises 29-38, compute the indicated...Ch. 3.6 - In Exercises 29-38, compute the indicated...Ch. 3.6 - In Exercises 29-38, compute the indicated...Ch. 3.6 - In Exercises 29-38, compute the indicated...Ch. 3.6 - In Exercises 29-38, compute the indicated...Ch. 3.6 - In Exercises 29-38, compute the indicated...Ch. 3.6 - In Exercises 29-38, compute the indicated...Ch. 3.6 - In Exercises 29-38, compute the indicated...Ch. 3.6 - In Exercises39-44, find the equation of the...Ch. 3.6 - In Exercises39-44, find the equation of the...Ch. 3.6 - In Exercises39-44, find the equation of the...Ch. 3.6 - In Exercises39-44, find the equation of the...Ch. 3.6 - In Exercises39-44, find the equation of the...Ch. 3.6 - In Exercises39-44, find the equation of the...Ch. 3.6 - Velocity If a stone is dropped from a height of...Ch. 3.6 - Velocity If a stone is dropped from a height of...Ch. 3.6 - Oil Imports from Mexico Daily crude oil imports to...Ch. 3.6 - Oil Imports from Mexico Daily crude oil production...Ch. 3.6 - Bottled Water Sales The following chart shows the...Ch. 3.6 - Bottled Water Sales The following chart shows...Ch. 3.6 - Ecology Increasing numbers of manatees have been...Ch. 3.6 - SAT Scores by Income The following graph shown...Ch. 3.6 - Television Advertising The cost, in thousands of...Ch. 3.6 - Television Advertising (Compare Exercises 53.) The...Ch. 3.6 - Of the three methods (numerical, graphical, and...Ch. 3.6 - Explain why we cannot put h=0 in the formula...Ch. 3.6 - You just got your derivatives test back, and you...Ch. 3.6 - Your friend just got his derivatives test back and...Ch. 3.6 - Your other friend just got her derivatives test...Ch. 3.6 - Your third friend just got her derivatives test...Ch. 3.6 - Your friend Muffy claims that, because the...Ch. 3.6 - Use the balanced difference quotient formula,...Ch. 3.6 - A certain function f has the property that f(a)...Ch. 3.6 - One cannot put h=0 in the formula...Ch. 3 - In Exercise 1-4, numerically estimate whether the...Ch. 3 - In Exercise 1-4, numerically estimate whether the...Ch. 3 - In Exercise 1-4, numerically estimate whether the...Ch. 3 - In Exercise 1-4, numerically estimate whether the...Ch. 3 - In Exercises 5 and 6 the graph of a function f is...Ch. 3 - In Exercises 5 and 6 the graph of a function f is...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 730, calculate the limit...Ch. 3 - In Exercises 31-34, find the average rate of...Ch. 3 - In Exercises 31-34, find the average rate of...Ch. 3 - In Exercises 31-34, find the average rate of...Ch. 3 - In Exercises 31-34, find the average rate of...Ch. 3 - In Exercise 35-38 you given the graph of a...Ch. 3 - In Exercise 35-38 you given the graph of a...Ch. 3 - In Exercise 35-38 you given the graph of a...Ch. 3 - In Exercise 35-38 you given the graph of a...Ch. 3 - Let f have the graph shown. Select the correct...Ch. 3 - Let f have the graph shown. Select the correct...Ch. 3 - In Exercises 4144, use the definition of the...Ch. 3 - In Exercises 4144, use the definition of the...Ch. 3 - In Exercises 4144, use the definition of the...Ch. 3 - In Exercises 4144, use the definition of the...Ch. 3 - In Exercises 4548, use technology to graph the...Ch. 3 - In Exercises 4548, use technology to graph the...Ch. 3 - In Exercises 4548, use technology to graph the...Ch. 3 - In Exercises 4548, use technology to graph the...Ch. 3 - Stock Investments OHaganBooks.com CEO John OHagan...Ch. 3 - Stock Investments John OHagans golf partner Juan...Ch. 3 - Real Estate Marjory Duffin has persuaded John...Ch. 3 - Advertising Costs OHaganBooks.com has (on further...Ch. 3 - Sales Since the start of July, OHaganBooks.com has...Ch. 3 - Rising Sea Level Marjory Duffin recently purchased...Ch. 3 - Real Estate The following graph (see Exercise 51)...Ch. 3 - Advertising Costs The following graph (see...Ch. 3 - Sales OHaganBooks.com fits the curve...Ch. 3 - Sea Levels Marjory Duffin fit the curve...Ch. 3 - Excluding subsidies, what should the annual...Ch. 3 - Excluding subsidies, what should the annual...Ch. 3 - What is the marginal emission charge (derivative...Ch. 3 - We said that the revised policy provided an...Ch. 3 - What change in C(q) wouldmake 8 million tons the...Ch. 3 - If the scenario in Exercise 5 took place, what...Ch. 3 - Because of intense lobbying by the utility...Ch. 3 - Suppose that instead of imposing a fixed charge...

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