Calculus & Its Applications
Calculus & Its Applications
15th Edition
ISBN: 9780137590896
Author: Larry J. Goldstein; David C. Lay; David I. Schneider; Nakhle H. Asmar; William Edward Tavernetti
Publisher: Pearson Education (US)
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Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…
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Chapter 3.1, Problem 51E
To determine

The rate at which the area of rectangle is increasing when width is 5 inches and length is 6 inches, where the width of the rectangle is increasing at a rate of 3 inches per second and its length is increasing at the rate of 4 inches per second.

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Chapter 3 Solutions

Calculus & Its Applications

Ch. 3.1 - Consider the function y=(x+1)x. Differentiate y by...Ch. 3.1 - Prob. 2CYUCh. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28. y=xxCh. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28. y=[...
Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Prob. 18ECh. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28. y=[...Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Find the equation of the tangent line to the curve...Ch. 3.1 - Find the equation of the tangent line to the curve...Ch. 3.1 - Find all x-coordinates of points (x,y) on the...Ch. 3.1 - Find the inflection points on the graph of...Ch. 3.1 - Find all x such that dydx=0, where...Ch. 3.1 - The graph of y=(x21)4(x2+1)5 is shown in Fig. 3....Ch. 3.1 - Find the point(s) on the graph of y=(x2+3x1)/x...Ch. 3.1 - Find the point(s) on the graph of y=(2x4+1)(x5)...Ch. 3.1 - Find d2ydx2. y=(x2+1)4Ch. 3.1 - Find d2ydx2. y=x2+1Ch. 3.1 - Find d2ydx2 y=xx+1Ch. 3.1 - Find d2ydx2 y=22+x2Ch. 3.1 - In Exercises 4144, a function h(x) is defined in...Ch. 3.1 - In Exercises 4144, a function h(x) is defined in...Ch. 3.1 - In Exercises 4144, a function h(x) is defined in...Ch. 3.1 - In Exercises 4144, a function h(x) is defined in...Ch. 3.1 - Volume An open rectangular box is 3 feet long and...Ch. 3.1 - Volume A closed rectangular box is to be...Ch. 3.1 - Prob. 47ECh. 3.1 - Prob. 48ECh. 3.1 - Average Revenue Let R(x) be the revenue received...Ch. 3.1 - Average Velocity Let s(t) be the number of miles a...Ch. 3.1 - Prob. 51ECh. 3.1 - Cost-Benefit of Emission Control A manufacturer...Ch. 3.1 - In Exercises 53 and 54, use the fact that at the...Ch. 3.1 - Prob. 54ECh. 3.1 - Prob. 55ECh. 3.1 - Prob. 56ECh. 3.1 - Prob. 57ECh. 3.1 - Prob. 58ECh. 3.1 - Prob. 59ECh. 3.1 - If f(x) and g(x) are differentiable functions such...Ch. 3.1 - If f(x) and g(x) are differentiable functions such...Ch. 3.1 - Prob. 62ECh. 3.1 - Let f(x)=1/x and g(x)=x3. Show that the product...Ch. 3.1 - Prob. 64ECh. 3.1 - Prob. 65ECh. 3.1 - Prob. 66ECh. 3.1 - Prob. 67ECh. 3.1 - Prob. 68ECh. 3.1 - Prob. 69ECh. 3.2 - Consider the function h(x)=(2x35)5+(2x35)4 Write...Ch. 3.2 - Consider the function h(x)=(2x35)5+(2x35)4 Compute...Ch. 3.2 - Prob. 3CYUCh. 3.2 - Compute f(g(x)), where f(x) and g(x) are the...Ch. 3.2 - Compute f(g(x)), where f(x) and g(x) are the...Ch. 3.2 - Compute f(g(x)), where f(x) and g(x) are the...Ch. 3.2 - Compute f(g(x)), where f(x) and g(x) are the...Ch. 3.2 - Each of following functions may be viewed as a...Ch. 3.2 - Each of following functions may be viewed as a...Ch. 3.2 - Each of following functions may be viewed as a...Ch. 3.2 - Each of following functions may be viewed as a...Ch. 3.2 - Each of following functions may be viewed as a...Ch. 3.2 - Each of following functions may be viewed as a...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - In Exercises 2126, a function h(x) is defined in...Ch. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - In Exercises 2126, a function h(x) is defined in...Ch. 3.2 - In Exercises 2126, a function h(x) is defined in...Ch. 3.2 - Prob. 26ECh. 3.2 - Sketch the graph of y=4x/(x+1)2,x1.Ch. 3.2 - Sketch the graph of y=2/(1+x2)Ch. 3.2 - Compute ddxf(g(x)), where f(x) and g(x) are...Ch. 3.2 - Compute ddxf(g(x)), where f(x) and g(x) are...Ch. 3.2 - Compute ddxf(g(x)), where f(x) and g(x) are...Ch. 3.2 - Compute ddxf(g(x)), where f(x) and g(x) are...Ch. 3.2 - Compute ddxf(g(x)), where f(x) and g(x) are...Ch. 3.2 - Compute ddxf(g(x)), where f(x) and g(x) are...Ch. 3.2 - Compute ddxf(g(x)), where f(x) and g(x) are...Ch. 3.2 - Compute ddxf(g(x)), where f(x) and g(x) are...Ch. 3.2 - Compute dydx using the chain rule in formula (1)....Ch. 3.2 - Compute dydx using the chain rule in formula (1)....Ch. 3.2 - Compute dydx using the chain rule in formula (1)....Ch. 3.2 - Prob. 40ECh. 3.2 - Compute dydxt=t0 y=x23x,x=t2+3,t0=0Ch. 3.2 - Compute dydxt=t0 y=(x22x+4)2,x=1t+1,t0=1Ch. 3.2 - Compute dydxt=t0 y=x+1x1,x=t24,t0=3Ch. 3.2 - Prob. 44ECh. 3.2 - Find the equation of the line tangent to the graph...Ch. 3.2 - Find the equation of the line tangent to the graph...Ch. 3.2 - Find the x- coordinate of all points on the curve...Ch. 3.2 - The function f(x)=x26x+10 has one relative minimum...Ch. 3.2 - Prob. 49ECh. 3.2 - Allometric Equation Many relations in biology are...Ch. 3.2 - Suppose that P, y and t are variables, where P is...Ch. 3.2 - Suppose that Q, x and y are variables, where Q is...Ch. 3.2 - Marginal Profit and Times Rate of Change When a...Ch. 3.2 - Marginal Cost and Time Rate of Change The cost of...Ch. 3.2 - A model for Carbon Monoxide Levels Ecologists...Ch. 3.2 - Profit A manufacturer of microcomputers estimates...Ch. 3.2 - Prob. 57ECh. 3.2 - Prob. 58ECh. 3.2 - If f(x) and g(x) are differentiable functions,...Ch. 3.2 - Prob. 60ECh. 3.2 - Effect of Stocks on Total Assets of a Company...Ch. 3.2 - Refer to Exercise 61. Use chain rule to find...Ch. 3.2 - Refer to Exercise 61. Find dxdt|t=2.5 and...Ch. 3.2 - Refer to Exercise 61. What was the maximum value...Ch. 3.2 - In an expression of the form f(g(x)), f(x) is...Ch. 3.3 - Solution can be found following the section...Ch. 3.3 - Solution can be found following the section...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - Use implicit differentiation of the equation in...Ch. 3.3 - Use implicit differentiation of the equation in...Ch. 3.3 - Use implicit differentiation of the equation in...Ch. 3.3 - Use implicit differentiation of the equation in...Ch. 3.3 - Use implicit differentiation of the equation in...Ch. 3.3 - Use implicit differentiation of the equation in...Ch. 3.3 - Find the equation of the tangent line to the graph...Ch. 3.3 - Find the equation of the tangent line to the graph...Ch. 3.3 - Slope of the Lemniscate The graph of...Ch. 3.3 - The graph of x4+2x2y2+y4=9x29y2 is a lemniscate...Ch. 3.3 - Marginal Rate of Substitution Suppose that x and y...Ch. 3.3 - Demand Equation Suppose that x and y represents...Ch. 3.3 - In Exercise 31 36, suppose that x and y are both...Ch. 3.3 - In Exercise 31 36, suppose that x and y are both...Ch. 3.3 - In Exercise 31 36, suppose that x and y are both...Ch. 3.3 - Prob. 34ECh. 3.3 - In Exercise 31 36, suppose that x and y are both...Ch. 3.3 - Prob. 36ECh. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Demand Equation Suppose that the price p (in...Ch. 3.3 - Demand Equation Suppose that the price p (in...Ch. 3.3 - Advertising Affects Revenue The monthly...Ch. 3.3 - Rate of Change of Price Suppose that in Boston the...Ch. 3.3 - Related Rates Figure 7 shows a 10- foot ladder...Ch. 3.3 - Related Rates An airplane flying 390 feet per...Ch. 3.3 - Related Rates A baseball diamond is a 90- foot by...Ch. 3.3 - Related Rates A motorcyclist is driving over a...Ch. 3 - State the product rule and quotient rule.Ch. 3 - Prob. 2FCCECh. 3 - Prob. 3FCCECh. 3 - Prob. 4FCCECh. 3 - Prob. 5FCCECh. 3 - Prob. 6FCCECh. 3 - Differentiate the following functions....Ch. 3 - Differentiate the following functions....Ch. 3 - Differentiate the following functions. y=x(x51)3Ch. 3 - Differentiate the following functions....Ch. 3 - Differentiate the following functions....Ch. 3 - Differentiate the following functions. y=xx+4Ch. 3 - Differentiate the following functions....Ch. 3 - Differentiate the following functions....Ch. 3 - Differentiate the following functions. y=x26xx2Ch. 3 - Differentiate the following functions. y=2x23xCh. 3 - Differentiate the following functions. y=(3x2x3)2Ch. 3 - Differentiate the following functions. y=x3+xx2xCh. 3 - Let f(x)=(3x+1)4(3x)5. Find all x such that...Ch. 3 - Let f(x)=x2+1x2+5. Find all x such that f(x)=0.Ch. 3 - Find the equation of the line tangent to the graph...Ch. 3 - Find the equation of the line tangent to the graph...Ch. 3 - Minimizing Area A botanical display is to be...Ch. 3 - Repeat Exercise 17, with the sidewalk on the...Ch. 3 - Cost function A store estimates that its cost when...Ch. 3 - Rate of Change of Taxes A company pays y dollars...Ch. 3 - In Exercise 21-23, find a formula for ddxf(g(x)),...Ch. 3 - In Exercise 21-23, find a formula for ddxf(g(x)),...Ch. 3 - In Exercise 21-23, find a formula for ddxf(g(x)),...Ch. 3 - In Exercise 24-26, find a formula for ddxf(g(x)),...Ch. 3 - In Exercise 24-26, find a formula for ddxf(g(x)),...Ch. 3 - In Exercise 24-26, find a formula for ddxf(g(x)),...Ch. 3 - In Exercise 27-29, find dydx, where y is a...Ch. 3 - In Exercise 27-29, find dydx, where y is a...Ch. 3 - In Exercise 27-29, find dydx, where y is a...Ch. 3 - In Exercises 30 32, find dydx, where y is a...Ch. 3 - In Exercises 30 32, find dydx, where y is a...Ch. 3 - In Exercises 30 32, find dydx, where y is a...Ch. 3 - Exercises 33 38 refer to the graphs of the...Ch. 3 - Exercises 33 38 refer to the graphs of the...Ch. 3 - Exercises 33 38 refer to the graphs of the...Ch. 3 - Exercises 33 38 refer to the graphs of the...Ch. 3 - Exercises 33 38 refer to the graphs of the...Ch. 3 - Exercises 33 38 refer to the graphs of the...Ch. 3 - Revenue Function The revenue, R, that a company...Ch. 3 - Amount of Drug Usage The amount, A, of anesthetics...Ch. 3 - The graph of x2/3+y2/3=8 is the astroid in Fig. 3...Ch. 3 - Slope of the Folium of Descartes The graph of...Ch. 3 - Slope of the Folium of Descartes The graph of...Ch. 3 - In Exercises 43-46, x and y are related by the...Ch. 3 - In Exercises 43-46, x and y are related by the...Ch. 3 - In Exercises 43-46, x and y are related by the...Ch. 3 - Cost Analysis and Production A factorys weekly...Ch. 3 - Use of Books at a Library A town library estimates...Ch. 3 - Demand equation Suppose that the price p and...Ch. 3 - Volume of an Oil Spill An offshore oil well is...Ch. 3 - Weight and Surface Area Animal physiologists have...Ch. 3 - Sales and Advertising Suppose that a kitchen...
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