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10th Edition

Soo T. Tan

Publisher: Brooks Cole

ISBN: 9781285464640

Chapter 3.6, Problem 74E

Textbook Problem

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In Exercises 69-74. determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.

**74.** If *h* is small in comparison to *a*, then

To determine

The statement “{If
h
is small in comparison to
a
, then
( a + h ) 1 3 ≈ a 1 3 + h 3 a 2 3
}” is true or false.

Expand the term

Substitute *a* for *x*, *y* for *h* and
*n* in above equation.

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

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What is the second derivative of a function f?...Ch. 3.5 - If s = f(t) gives the position of an object moving...Ch. 3.5 - Suppose f(t) measures the population of a country...Ch. 3.5 - Suppose f(t) measures the population of a country...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 1-20, find the first and second...Ch. 3.5 - In Exercises 21-28, find the third derivative of...Ch. 3.5 - In Exercises 21-28, find the third derivative of...Ch. 3.5 - In Exercises 21-28, find the third derivative of...Ch. 3.5 - In Exercises 21-28, find the third derivative of...Ch. 3.5 - In Exercises 21-28, find the third derivative of...Ch. 3.5 - In Exercises 21-28, find the third derivative of...Ch. 3.5 - In Exercises 21-28, find the third derivative of...Ch. 3.5 - In Exercises 21-28, find the third derivative of...Ch. 3.5 - acceleration of a falling object During the...Ch. 3.5 - acceleration of a car The distance s (in feet)...Ch. 3.5 - auto transmissions .and fuel economy In trying to...Ch. 3.5 - Alzheimer'S Disease As baby boomers enter their...Ch. 3.5 - Crime Rates The number of major crimes committed...Ch. 3.5 - gdp of a developing country A developing countrys...Ch. 3.5 - sales of vinyl records Vinyl records (LPs) almost...Ch. 3.5 - Median Age of U.S. Population The median age (in...Ch. 3.5 - Obesity in America The body mass index (BMI)...Ch. 3.5 - Test Flight of a Vtol In a test flight of the...Ch. 3.5 - Air Purification During testing of a certain brand...Ch. 3.5 - WORKING MOTHERS The percentage of mothers who work...Ch. 3.5 - AGING POPULATION The population of Americans age...Ch. 3.5 - In Exercises 42-46, determine whether the...Ch. 3.5 - In Exercises 42-46, determine whether the...Ch. 3.5 - In Exercises 42-46, determine whether the...Ch. 3.5 - In Exercises 42-46, determine whether the...Ch. 3.5 - In Exercises 42-46, determine whether the...Ch. 3.5 - LetC(x) be the average cost function associated...Ch. 3.5 - Let f be the function defined by the rule f(x) =...Ch. 3.5 - Construct a function f that has derivatives of...Ch. 3.5 - Show that a polynomial function has derivatives of...Ch. 3.5 - In Exercises 1-8, find the value of the second...Ch. 3.5 - In Exercises 1-8, find the value of the second...Ch. 3.5 - In Exercises 1-8, find the value of the second...Ch. 3.5 - In Exercises 1-8, find the value of the second...Ch. 3.5 - In Exercises 1-8, find the value of the second...Ch. 3.5 - In Exercises 1-8, find the value of the second...Ch. 3.5 - In Exercises 1-8, find the value of the second...Ch. 3.5 - In Exercises 1-8, find the value of the second...Ch. 3.6 - a. Suppose the equation F(x, y) = 0 defines y as a...Ch. 3.6 - Suppose the equation xg(y) + yf(x) = 0, where f...Ch. 3.6 - In your own words, describe what a related-rates...Ch. 3.6 - Give the steps that you would use to solve a...Ch. 3.6 - In Exercises 1-8, find the derivative dy/dx (a) by...Ch. 3.6 - In Exercises 1-8, find the derivative dy/dx (a) by...Ch. 3.6 - In Exercises 1-8, find the derivative dy/dx (a) by...Ch. 3.6 - In Exercises 1-8, find the derivative dy/dx (a) by...Ch. 3.6 - In Exercises 1-8, find the derivative dy/dx (a) by...Ch. 3.6 - In Exercises 1-8, find the derivative dy/dx (a) by...Ch. 3.6 - In Exercises 1-8, find the derivative dy/dx (a) by...Ch. 3.6 - In Exercises 1-8, find the derivative dy/dx (a) by...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 9-30, find dy/dx by implicit...Ch. 3.6 - In Exercises 31-34, find an equation of the...Ch. 3.6 - In Exercises 31-34, find an equation of the...Ch. 3.6 - In Exercises 31-34, find an equation of the...Ch. 3.6 - In Exercises 31-34, find an equation of the...Ch. 3.6 - In Exercises 35-38, find the second derivative...Ch. 3.6 - In Exercises 35-38, find the second derivative...Ch. 3.6 - In Exercises 35-38, find the second derivative...Ch. 3.6 - In Exercises 35-38, find the second derivative...Ch. 3.6 - Volume of a Cylinder The volume of a...Ch. 3.6 - Distance Between Two Cars A car leaves an...Ch. 3.6 - Effect of Price on Demand for Tires Suppose the...Ch. 3.6 - Effect of Price on Supply of Tires Suppose the...Ch. 3.6 - Effect of Price on Demand for Headphones The...Ch. 3.6 - Effect of Price on Supply of Eggs Suppose the...Ch. 3.6 - Effect of Supply on price of Eggs Refer to...Ch. 3.6 - Elasticity of Demand for Ink-Jet Cartridges The...Ch. 3.6 - Elasticity of demand for CDs The demand function...Ch. 3.6 - Production Function for a Furniture Company The...Ch. 3.6 - Output of a Country Suppose that the output Q of a...Ch. 3.6 - Volume of a Cube The volume V of a cube with sides...Ch. 3.6 - Oil Spills In calm waters, the oil spilling from...Ch. 3.6 - Distance Between Two Ships Two ships leave the...Ch. 3.6 - Oil. Spills In calm waters, the oil spilling from...Ch. 3.6 - Distance Between Two Cars a car leaves an...Ch. 3.6 - Distance Between Two Cars a car leaves an...Ch. 3.6 - Watching a Helicopter Take off At a distance of 50...Ch. 3.6 - Watching a rowing Race a spectator watches a...Ch. 3.6 - Docking A Boat A boat is pulled toward a dock by...Ch. 3.6 - A Melting Snowball Assume that a snowball is in...Ch. 3.6 - Blowing soap Bubbles Carlos is blowing air into a...Ch. 3.6 - Coast Guard Patrol search mission The pilot of a...Ch. 3.6 - FILLING A COFFEE POT A coffee pot in the form of a...Ch. 3.6 - Movement of a Shadow A 6-ft tall man is walking...Ch. 3.6 - A Sliding Ladder A 20-ft ladder leaning against a...Ch. 3.6 - A Sliding Ladder The base of a 13-ft ladder...Ch. 3.6 - Flow of Water from a Tank Water flows from a tank...Ch. 3.6 - Volume of a Gas In an adiabatic process (one in...Ch. 3.6 - Mass of a Moving Particle The mass m of a panicle...Ch. 3.6 - In Exercises 69-74. determine whether the...Ch. 3.6 - In Exercises 69-74. determine whether the...Ch. 3.6 - In Exercises 69-74. determine whether the...Ch. 3.6 - In Exercises 69-74. determine whether the...Ch. 3.6 - In Exercises 69-74. determine whether the...Ch. 3.6 - In Exercises 69-74. determine whether the...Ch. 3.7 - 1. If y = y(x), what is the differential of x?...Ch. 3.7 - Refer to the following figure. a. Express A, B,...Ch. 3.7 - Suppose the population of a city at time t0 is...Ch. 3.7 - Suppose that the total profit of a company at time...Ch. 3.7 - In Exercises 1-14, find the differential of the...Ch. 3.7 - In Exercises 1-14, find the differential of the...Ch. 3.7 - In Exercises 1-14, find the differential of the...Ch. 3.7 - In Exercises 1-14, find the differential of the...Ch. 3.7 - In Exercises 1-14, find the differential of the...Ch. 3.7 - In Exercises 1-14, find the differential of the...Ch. 3.7 - In Exercises 1-14, find the differential of the...Ch. 3.7 - In Exercises 1-14, find the differential of the...Ch. 3.7 - In Exercises 1-14, find the differential of the...Ch. 3.7 - In Exercises 1-14, find the differential of the...Ch. 3.7 - In Exercises 1-14, find the differential of the...Ch. 3.7 - In Exercises 1-14, find the differential of the...Ch. 3.7 - In Exercises 1-14, find the differential of the...Ch. 3.7 - In Exercises 1-14, find the differential of the...Ch. 3.7 - Let f be the function defined by y = f(x) = x2 1...Ch. 3.7 - Let f be the function defined by y = f(x) 5 3x2 ...Ch. 3.7 - Let f be the function defined by y=f(x)=1x a. Find...Ch. 3.7 - Let f be the function defined by y=f(x)=2x+1 a....Ch. 3.7 - In Exercises 19-26, use differentials to...Ch. 3.7 - In Exercises 19-26, use differentials to...Ch. 3.7 - In Exercises 19-26, use differentials to...Ch. 3.7 - In Exercises 19-26, use differentials to...Ch. 3.7 - In Exercises 19-26, use differentials to...Ch. 3.7 - In Exercises 19-26, use differentials to...Ch. 3.7 - In Exercises 19-26, use differentials to...Ch. 3.7 - In Exercises 19-26, use differentials to...Ch. 3.7 - Use a differential to approximate 4.02+14.02.Ch. 3.7 - Use a differential to approximate...Ch. 3.7 - Error Estimation The length of each edge of a cube...Ch. 3.7 - Estimating the Amount of Paint Required A coat of...Ch. 3.7 - Estimating the Amount of Rust-Proofer Required A...Ch. 3.7 - Growth of a CANCEROUS tumor The volume of a...Ch. 3.7 - Unclogging arteries Research done in the 1930s by...Ch. 3.7 - effect of capital expenditures on gdp An economist...Ch. 3.7 - learning curves The length of time (in seconds) a...Ch. 3.7 - effect of advertising on profits The relationship...Ch. 3.7 - effect of mortgage rates on housing starts A study...Ch. 3.7 - Effect of Supply of Radios on Price The supply...Ch. 3.7 - Effect of demand for smoke alarms on price The...Ch. 3.7 - Surface area of an animal Animal physiologists use...Ch. 3.7 - Forecasting Profits The management of Trappee and...Ch. 3.7 - Forecasting Commodity Prices A certain countrys...Ch. 3.7 - Demand for Tires The management of Titan Tire...Ch. 3.7 - Air Pollution The amount of nitrogen dioxide, a...Ch. 3.7 - Effect of Community Investment on Crime A...Ch. 3.7 - Financing a Home The Millers are planning to buy a...Ch. 3.7 - Investments Lup deposits a sum of 10,000 into an...Ch. 3.7 - Defined Benefit accounts Ian, who is...Ch. 3.7 - In Exercises 49 and 50, determine whether the...Ch. 3.7 - In Exercises 49 and 50, determine whether the...Ch. 3.7 - In Exercises 1-6, use dy to approximate y for the...Ch. 3.7 - In Exercises 1-6, use dy to approximate y for the...Ch. 3.7 - In Exercises 1-6, use dy to approximate y for the...Ch. 3.7 - In Exercises 1-6, use dy to approximate y for the...Ch. 3.7 - In Exercises 1-6, use dy to approximate y for the...Ch. 3.7 - In Exercises 1-6, use dy to approximate y for the...Ch. 3.7 - Calculating Mortgage Payments Refer to Example 2....Ch. 3.7 - Estimating THE Area ok a Ring of Neptune The ring...Ch. 3 - a. If c is a constant, then ddx(c)=__________. b....Ch. 3 - a. The Product Rule states that...Ch. 3 - a. The Chain Rule states that if h(x) = g[f(x)],...Ch. 3 - If C, R, P, and C denote the total cost function,...Ch. 3 - a. If f is a differentiable demand function...Ch. 3 - Suppose a function y = f(x) is defined implicitly...Ch. 3 - In a related-rates problem, we are given a...Ch. 3 - Let y = f(t) and x = g(t). If x2 + y2 = 4, then...Ch. 3 - a. If a variable quantity x changes from x1 to x2,...Ch. 3 - If y = f(x), where f is a differentiable function,...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-20, find the first and second...Ch. 3 - In Exercises 1-20, find the first and second...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 1-30, find the derivative of the...Ch. 3 - In Exercises 31-36, find the second derivative of...Ch. 3 - In Exercises 31-36, find the second derivative of...Ch. 3 - In Exercises 31-36, find the second derivative of...Ch. 3 - In Exercises 31-36, find the second derivative of...Ch. 3 - In Exercises 31-36, find the second derivative of...Ch. 3 - In Exercises 31-36, find the second derivative of...Ch. 3 - In Exercises 37-42, find dy/dx by implicit...Ch. 3 - In Exercises 37-42, find dy/dx by implicit...Ch. 3 - In Exercises 37-42, find dy/dx by implicit...Ch. 3 - In Exercises 37-42, find dy/dx by implicit...Ch. 3 - In Exercises 37-42, find dy/dx by implicit...Ch. 3 - In Exercises 37-42, find dy/dx by implicit...Ch. 3 - Find the differential of f(x)=x2+1x2Ch. 3 - Find the differential of f(x)=1x3+1Ch. 3 - Let f be the function defined by f(x)=2x2+4 a....Ch. 3 - Use a differential to approximate 26.83Ch. 3 - Let f(x) = 2x3 3x2 16x + 3. a. Find the points...Ch. 3 - Find an equation of the tangent line to the graph...Ch. 3 - Find an equation of the tangent line to the graph...Ch. 3 - Find the third derivative of the function...Ch. 3 - SALES OF DSPs The annual sales of digital signal...Ch. 3 - U.k. Digital Video Viewers Digital video viewing...Ch. 3 - adult obesity In the United States, the percentage...Ch. 3 - Sales of Cameras The shipments of Lica digital...Ch. 3 - Gdp of a Country The gross domestic product (GDP)...Ch. 3 - Population Growth in A Suburb The population of a...Ch. 3 - Best-Selling Novel The number of copies of a...Ch. 3 - Cable TV Subscribers The number of subscribers to...Ch. 3 - Cost of Wireless Phone Calls As cellular phone...Ch. 3 - Male Life Expectancy Suppose the life expectancy...Ch. 3 - Cost of Producing DVDs The total weekly cost in...Ch. 3 - Supply Function for Satellite Radios The supply...Ch. 3 - Demand Function for Electric Shavers The demand...Ch. 3 - Marginal Cost The total daily cost (in dollars)...Ch. 3 - Demand for Smartphones The marketing department of...Ch. 3 - Demand for Photocopying Machines The weekly demand...Ch. 3 - Marginal Average Cost The Custom Office makes a...Ch. 3 - Elasticity of Demand The demand equation for a...Ch. 3 - Elasticity of Demand The demand equation for a...Ch. 3 - Elasticity OF Demand The demand equation for a...Ch. 3 - Elasticity of Demand The demand equation for a...Ch. 3 - GDP of a Country The GDP of a country from the...Ch. 3 - Motion of an Object The position of an object...Ch. 3 - Find the derivative of f(x) = 2x3 3x1/3 + 5x2/3.Ch. 3 - Differentiateg(x)=x2x21Ch. 3 - Find dydx if y=2x+1x2+x+1Ch. 3 - Find the first three derivatives of, f(x)=1x+1Ch. 3 - Find dydx given that xy2 x2y + x3 = 4.Ch. 3 - Let y=xx2+5 a. Find the differential of y. b. If x...

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