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Applied Calculus

7th Edition
Waner + 1 other
Publisher: Cengage Learning,
ISBN: 9781337291248

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Section
BuyFindarrow_forward

Applied Calculus

7th Edition
Waner + 1 other
Publisher: Cengage Learning,
ISBN: 9781337291248
Chapter 3.6, Problem 29E
Textbook Problem
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In Exercises 29-38, compute the indicated derivative.

R ( t ) = 0.3 t 2 ; R ( 2 )

To determine

To calculate: The value of the derivative R(2) for the function R(t)=0.3t2.

Explanation of Solution

Given Information:

The provided function is R(t)=0.3t2.

Formula used:

The difference quotient formula is used which is as follows:

f(a)=limh0f(a+h)f(a)h

The square of the sum formula,

(a+b)2=a2+b2+2ab

Calculation:

Consider the function, R(t)=0.3t2

The difference quotient formula used to estimate the exact value of derivative algebraically is:

f(a)=limh0f(a+h)f(a)h

But, according to the question,

R(a)=limh0R(a+h)R(a)h

Substitute a=2 into the above formula,

R(2)=limh0R(2+h)R(2)h

Here R(2)=0.3(2)2 then,

R(2+h)=0.3(2+h)2

Substitute the values of R(2) and R(2+h) in the formula R(2)=limh0R(2+h)R(2)h as,

R(2)=limh0[(0

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Applied Calculus
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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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