Student Solutions Manual For Larson/edwards' Calculus Of A Single Variable: Early Transcendental Functions, 2nd
7th Edition
ISBN: 9781337552561
Author: Ron Larson, Bruce H. Edwards
Publisher: Cengage Learning
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Textbook Question
Chapter 5.7, Problem 97E
Maximizing an Angle In the figure, find the value of c in the interval
![Chapter 5.7, Problem 97E, Maximizing an Angle In the figure, find the value of c in the interval [0,4] on the x-axis that](https://content.bartleby.com/tbms-images/9781337275361/Chapter-5/images/75361-5.7-97e-question-digital_image350.png)
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Chapter 5 Solutions
Student Solutions Manual For Larson/edwards' Calculus Of A Single Variable: Early Transcendental Functions, 2nd
Ch. 5.1 - Natural Logarithmic Function Explain why ln x is...Ch. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Evaluating a Logarithm Using Technology In...Ch. 5.1 - Prob. 8ECh. 5.1 - Matching In Exercises 912, match the function with...Ch. 5.1 - Prob. 10E
Ch. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Sketching the Graph In Exercises 13-18, sketch the...Ch. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Expanding a Logarithmic Expression In Exercises...Ch. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Expanding a Logarithmic Expression In Exercises...Ch. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 37ECh. 5.1 - Prob. 38ECh. 5.1 - Prob. 39ECh. 5.1 - Finding a Limit In Exercises 39-42, find the...Ch. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Finding a Derivative In Exercises 43-66, find the...Ch. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Finding a Derivative In Exercises 43-66, find the...Ch. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Finding a Derivative In Exercises 43-66, find the...Ch. 5.1 - Prob. 55ECh. 5.1 - Prob. 56ECh. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Prob. 59ECh. 5.1 - Prob. 60ECh. 5.1 - Finding a Derivative In Exercises 43-66, find the...Ch. 5.1 - Prob. 62ECh. 5.1 - Prob. 63ECh. 5.1 - Finding a Derivative In Exercises 43-66, find the...Ch. 5.1 - Prob. 65ECh. 5.1 - Prob. 66ECh. 5.1 - Prob. 67ECh. 5.1 - Prob. 68ECh. 5.1 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.1 - Prob. 70ECh. 5.1 - Prob. 71ECh. 5.1 - Prob. 72ECh. 5.1 - Prob. 73ECh. 5.1 - Prob. 74ECh. 5.1 - Prob. 75ECh. 5.1 - Prob. 76ECh. 5.1 - Prob. 77ECh. 5.1 - Prob. 78ECh. 5.1 - Prob. 79ECh. 5.1 - Prob. 80ECh. 5.1 - Prob. 81ECh. 5.1 - Prob. 82ECh. 5.1 - Prob. 83ECh. 5.1 - Prob. 84ECh. 5.1 - Prob. 85ECh. 5.1 - Prob. 86ECh. 5.1 - Prob. 87ECh. 5.1 - Prob. 88ECh. 5.1 - Prob. 89ECh. 5.1 - Prob. 90ECh. 5.1 - Prob. 91ECh. 5.1 - Prob. 92ECh. 5.1 - Prob. 93ECh. 5.1 - Prob. 94ECh. 5.1 - Prob. 95ECh. 5.1 - Prob. 96ECh. 5.1 - Prob. 97ECh. 5.1 - Prob. 98ECh. 5.1 - Prob. 99ECh. 5.1 - Prob. 100ECh. 5.1 - Prob. 101ECh. 5.1 - Prob. 102ECh. 5.1 - Prob. 103ECh. 5.1 - Sound Intensity The relationship between the...Ch. 5.1 - Modeling Data The table shows the temperatures T...Ch. 5.1 - Prob. 106ECh. 5.1 - Prob. 107ECh. 5.1 - Prob. 108ECh. 5.1 - Prob. 109ECh. 5.2 - CONCEPT CHECK Log Rule for Integration Can you use...Ch. 5.2 - Prob. 2ECh. 5.2 - Prob. 3ECh. 5.2 - Prob. 4ECh. 5.2 - Finding an Indefinite Integral In Exercises 528,...Ch. 5.2 - Prob. 6ECh. 5.2 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.2 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.2 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.2 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.2 - Finding an Indefinite Integral In Exercises 528,...Ch. 5.2 - Finding an Indefinite Integral In Exercises 528,...Ch. 5.2 - Finding an Indefinite Integral In Exercises 528,...Ch. 5.2 - Finding an Indefinite Integral In Exercises 528,...Ch. 5.2 - Finding an Indefinite Integral In Exercises 528,...Ch. 5.2 - Prob. 16ECh. 5.2 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.2 - Prob. 18ECh. 5.2 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.2 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.2 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.2 - Prob. 22ECh. 5.2 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.2 - Prob. 24ECh. 5.2 - Prob. 25ECh. 5.2 - Prob. 26ECh. 5.2 - Prob. 27ECh. 5.2 - Finding an Indefinite Integral In Exercises 528,...Ch. 5.2 - Prob. 29ECh. 5.2 - Prob. 30ECh. 5.2 - Prob. 31ECh. 5.2 - Change of Variables In Exercises 2932, find the...Ch. 5.2 - Prob. 33ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 34ECh. 5.2 - Prob. 35ECh. 5.2 - Prob. 38ECh. 5.2 - Prob. 37ECh. 5.2 - Prob. 39ECh. 5.2 - Prob. 40ECh. 5.2 - Prob. 41ECh. 5.2 - Prob. 42ECh. 5.2 - Prob. 43ECh. 5.2 - Prob. 44ECh. 5.2 - Prob. 45ECh. 5.2 - Prob. 46ECh. 5.2 - Prob. 47ECh. 5.2 - Prob. 48ECh. 5.2 - Prob. 49ECh. 5.2 - Prob. 50ECh. 5.2 - Prob. 51ECh. 5.2 - Prob. 52ECh. 5.2 - Prob. 53ECh. 5.2 - Prob. 54ECh. 5.2 - Prob. 55ECh. 5.2 - Prob. 56ECh. 5.2 - Prob. 57ECh. 5.2 - Prob. 58ECh. 5.2 - Prob. 59ECh. 5.2 - Finding an Integral Using Technology In Exercises...Ch. 5.2 - Prob. 61ECh. 5.2 - Prob. 62ECh. 5.2 - Prob. 63ECh. 5.2 - Prob. 64ECh. 5.2 - Prob. 65ECh. 5.2 - Prob. 66ECh. 5.2 - Prob. 67ECh. 5.2 - Prob. 68ECh. 5.2 - Prob. 69ECh. 5.2 - Area In Exercises 69-72, find the area of the...Ch. 5.2 - Prob. 71ECh. 5.2 - Prob. 72ECh. 5.2 - Finding the Average Value of a Function In...Ch. 5.2 - Prob. 74ECh. 5.2 - Prob. 75ECh. 5.2 - Prob. 76ECh. 5.2 - Prob. 77ECh. 5.2 - Prob. 78ECh. 5.2 - Prob. 79ECh. 5.2 - Prob. 80ECh. 5.2 - Napier's Inequality For 0 x y, use the Mean...Ch. 5.2 - Prob. 82ECh. 5.2 - Prob. 83ECh. 5.2 - Prob. 84ECh. 5.2 - Prob. 85ECh. 5.2 - Prob. 86ECh. 5.2 - Prob. 87ECh. 5.2 - Prob. 88ECh. 5.2 - Prob. 89ECh. 5.2 - Prob. 90ECh. 5.2 - Prob. 91ECh. 5.2 - Prob. 92ECh. 5.2 - Prob. 93ECh. 5.2 - Prob. 94ECh. 5.2 - Prob. 95ECh. 5.2 - Prob. 96ECh. 5.2 - Prob. 97ECh. 5.2 - Prob. 98ECh. 5.2 - Prob. 99ECh. 5.2 - Prob. 100ECh. 5.2 - Prob. 101ECh. 5.3 - Inverse Functions In your own words, describe what...Ch. 5.3 - Reflective Property of Inverse Functions Describe...Ch. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Matching In Exercises 5-8, match the graph of the...Ch. 5.3 - Prob. 6ECh. 5.3 - Prob. 7ECh. 5.3 - Prob. 8ECh. 5.3 - Prob. 9ECh. 5.3 - Prob. 10ECh. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Prob. 16ECh. 5.3 - Prob. 17ECh. 5.3 - Prob. 18ECh. 5.3 - Prob. 19ECh. 5.3 - Prob. 20ECh. 5.3 - Prob. 21ECh. 5.3 - Prob. 22ECh. 5.3 - Prob. 23ECh. 5.3 - Prob. 24ECh. 5.3 - Prob. 25ECh. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.3 - Prob. 30ECh. 5.3 - Prob. 31ECh. 5.3 - Prob. 32ECh. 5.3 - Prob. 33ECh. 5.3 - Prob. 34ECh. 5.3 - Prob. 35ECh. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - Prob. 38ECh. 5.3 - Prob. 39ECh. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - Prob. 43ECh. 5.3 - Prob. 44ECh. 5.3 - Prob. 45ECh. 5.3 - Prob. 46ECh. 5.3 - Prob. 47ECh. 5.3 - Finding an Inverse Function In Exercises 47 and...Ch. 5.3 - Cost You need a total of 50 pounds of two...Ch. 5.3 - Prob. 50ECh. 5.3 - Prob. 51ECh. 5.3 - Prob. 52ECh. 5.3 - Prob. 53ECh. 5.3 - Prob. 54ECh. 5.3 - Prob. 55ECh. 5.3 - Making a Function One-to-One In Exercises 55-58,...Ch. 5.3 - Prob. 57ECh. 5.3 - Prob. 58ECh. 5.3 - Prob. 59ECh. 5.3 - Prob. 60ECh. 5.3 - Prob. 61ECh. 5.3 - Prob. 62ECh. 5.3 - Prob. 63ECh. 5.3 - Prob. 64ECh. 5.3 - Evaluating the Derivative of an Inverse Function...Ch. 5.3 - Prob. 66ECh. 5.3 - Prob. 67ECh. 5.3 - Prob. 68ECh. 5.3 - Prob. 69ECh. 5.3 - Prob. 70ECh. 5.3 - Prob. 71ECh. 5.3 - Prob. 72ECh. 5.3 - Prob. 73ECh. 5.3 - Prob. 74ECh. 5.3 - Prob. 75ECh. 5.3 - Prob. 76ECh. 5.3 - Prob. 77ECh. 5.3 - Prob. 78ECh. 5.3 - Prob. 79ECh. 5.3 - Prob. 80ECh. 5.3 - Prob. 81ECh. 5.3 - Prob. 82ECh. 5.3 - Inverse Function Consider the function f(x)=xn...Ch. 5.3 - Prob. 84ECh. 5.3 - Prob. 85ECh. 5.3 - Prob. 86ECh. 5.3 - Prob. 87ECh. 5.3 - Prob. 88ECh. 5.3 - Prob. 89ECh. 5.3 - Prob. 90ECh. 5.3 - Prob. 91ECh. 5.3 - Prob. 92ECh. 5.3 - Prob. 93ECh. 5.3 - Prob. 94ECh. 5.3 - Prob. 95ECh. 5.3 - Prob. 96ECh. 5.3 - Prob. 97ECh. 5.3 - Prob. 98ECh. 5.3 - Prob. 99ECh. 5.3 - Prob. 100ECh. 5.3 - Prob. 101ECh. 5.4 - Natural Exponential Function of Describe the graph...Ch. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Prob. 5ECh. 5.4 - Prob. 6ECh. 5.4 - Prob. 7ECh. 5.4 - Prob. 8ECh. 5.4 - Prob. 9ECh. 5.4 - Prob. 10ECh. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Prob. 12ECh. 5.4 - Prob. 13ECh. 5.4 - Prob. 14ECh. 5.4 - Prob. 15ECh. 5.4 - Prob. 16ECh. 5.4 - Prob. 17ECh. 5.4 - Prob. 18ECh. 5.4 - Prob. 19ECh. 5.4 - Prob. 20ECh. 5.4 - Prob. 21ECh. 5.4 - Prob. 22ECh. 5.4 - Prob. 23ECh. 5.4 - Prob. 24ECh. 5.4 - Prob. 25ECh. 5.4 - Prob. 26ECh. 5.4 - Prob. 27ECh. 5.4 - Prob. 28ECh. 5.4 - Prob. 29ECh. 5.4 - Prob. 30ECh. 5.4 - Prob. 31ECh. 5.4 - Prob. 32ECh. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Prob. 42ECh. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Prob. 44ECh. 5.4 - Prob. 45ECh. 5.4 - Prob. 46ECh. 5.4 - Prob. 47ECh. 5.4 - Prob. 48ECh. 5.4 - Prob. 49ECh. 5.4 - Prob. 50ECh. 5.4 - Prob. 51ECh. 5.4 - Prob. 52ECh. 5.4 - Prob. 53ECh. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Prob. 55ECh. 5.4 - Prob. 56ECh. 5.4 - Prob. 57ECh. 5.4 - Prob. 58ECh. 5.4 - Prob. 59ECh. 5.4 - Prob. 60ECh. 5.4 - Prob. 61ECh. 5.4 - Prob. 62ECh. 5.4 - Prob. 63ECh. 5.4 - Prob. 64ECh. 5.4 - Finding the Equation of a Tangent Line In...Ch. 5.4 - Prob. 66ECh. 5.4 - Prob. 67ECh. 5.4 - Prob. 68ECh. 5.4 - Prob. 69ECh. 5.4 - Prob. 70ECh. 5.4 - Prob. 71ECh. 5.4 - Prob. 72ECh. 5.4 - Prob. 73ECh. 5.4 - Prob. 74ECh. 5.4 - Prob. 75ECh. 5.4 - Prob. 76ECh. 5.4 - Prob. 77ECh. 5.4 - Prob. 78ECh. 5.4 - Area Find the area of the largest rectangle that...Ch. 5.4 - Prob. 80ECh. 5.4 - Prob. 81ECh. 5.4 - Prob. 82ECh. 5.4 - Prob. 83ECh. 5.4 - Prob. 84ECh. 5.4 - Prob. 85ECh. 5.4 - Prob. 86ECh. 5.4 - Prob. 87ECh. 5.4 - Prob. 88ECh. 5.4 - Prob. 89ECh. 5.4 - Prob. 90ECh. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Prob. 92ECh. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Prob. 94ECh. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Prob. 96ECh. 5.4 - Prob. 97ECh. 5.4 - Prob. 98ECh. 5.4 - Prob. 99ECh. 5.4 - Prob. 100ECh. 5.4 - Prob. 101ECh. 5.4 - Prob. 102ECh. 5.4 - Prob. 103ECh. 5.4 - Prob. 104ECh. 5.4 - Prob. 105ECh. 5.4 - Prob. 106ECh. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Prob. 108ECh. 5.4 - Prob. 109ECh. 5.4 - Prob. 110ECh. 5.4 - Prob. 111ECh. 5.4 - Prob. 112ECh. 5.4 - Prob. 113ECh. 5.4 - Prob. 114ECh. 5.4 - Prob. 115ECh. 5.4 - Prob. 116ECh. 5.4 - Prob. 117ECh. 5.4 - Prob. 118ECh. 5.4 - Prob. 119ECh. 5.4 - Prob. 120ECh. 5.4 - Prob. 121ECh. 5.4 - Prob. 122ECh. 5.4 - Prob. 123ECh. 5.4 - Prob. 124ECh. 5.4 - Prob. 125ECh. 5.4 - Prob. 126ECh. 5.4 - Prob. 127ECh. 5.4 - Prob. 128ECh. 5.4 - Prob. 129ECh. 5.4 - Prob. 130ECh. 5.4 - Prob. 131ECh. 5.4 - Prob. 132ECh. 5.4 - Prob. 133ECh. 5.4 - Prob. 134ECh. 5.4 - Probability A car battery has an average lifetime...Ch. 5.4 - Probability The median waiting time (in minutes)...Ch. 5.4 - Prob. 137ECh. 5.4 - Prob. 138ECh. 5.4 - Prob. 139ECh. 5.4 - Prob. 140ECh. 5.4 - Prob. 141ECh. 5.4 - Prob. 142ECh. 5.4 - Prob. 143ECh. 5.4 - Prob. 144ECh. 5.4 - Prob. 145ECh. 5.5 - Prob. 1ECh. 5.5 - Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.5 - Prob. 6ECh. 5.5 - Prob. 7ECh. 5.5 - Prob. 8ECh. 5.5 - Prob. 9ECh. 5.5 - Prob. 10ECh. 5.5 - Prob. 11ECh. 5.5 - Prob. 12ECh. 5.5 - Prob. 13ECh. 5.5 - Prob. 14ECh. 5.5 - Prob. 15ECh. 5.5 - Prob. 16ECh. 5.5 - Prob. 17ECh. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.5 - Prob. 20ECh. 5.5 - Prob. 21ECh. 5.5 - Prob. 22ECh. 5.5 - Prob. 23ECh. 5.5 - Prob. 24ECh. 5.5 - Solving an Equation In Exercises 21-26, solve for...Ch. 5.5 - Prob. 26ECh. 5.5 - Prob. 27ECh. 5.5 - Prob. 28ECh. 5.5 - Prob. 29ECh. 5.5 - Prob. 30ECh. 5.5 - Prob. 31ECh. 5.5 - Prob. 32ECh. 5.5 - Prob. 33ECh. 5.5 - Prob. 34ECh. 5.5 - Prob. 35ECh. 5.5 - Prob. 36ECh. 5.5 - Prob. 37ECh. 5.5 - Prob. 38ECh. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Prob. 40ECh. 5.5 - Prob. 41ECh. 5.5 - Prob. 42ECh. 5.5 - Prob. 43ECh. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Prob. 45ECh. 5.5 - Prob. 46ECh. 5.5 - Prob. 47ECh. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Prob. 49ECh. 5.5 - Prob. 50ECh. 5.5 - Prob. 51ECh. 5.5 - Prob. 52ECh. 5.5 - Prob. 53ECh. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Prob. 56ECh. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Prob. 59ECh. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Prob. 61ECh. 5.5 - Prob. 62ECh. 5.5 - Prob. 63ECh. 5.5 - Prob. 64ECh. 5.5 - Logarithmic Differentiation In Exercises 65-68,...Ch. 5.5 - Prob. 66ECh. 5.5 - Prob. 67ECh. 5.5 - Prob. 68ECh. 5.5 - Prob. 69ECh. 5.5 - Prob. 70ECh. 5.5 - Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Prob. 73ECh. 5.5 - Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Prob. 77ECh. 5.5 - Prob. 78ECh. 5.5 - Prob. 79ECh. 5.5 - Evaluating a Definite Integral In Exercises 77-80,...Ch. 5.5 - Prob. 81ECh. 5.5 - Prob. 82ECh. 5.5 - Prob. 83ECh. 5.5 - Prob. 84ECh. 5.5 - Prob. 85ECh. 5.5 - Prob. 86ECh. 5.5 - Prob. 87ECh. 5.5 - Prob. 88ECh. 5.5 - Prob. 89ECh. 5.5 - Prob. 90ECh. 5.5 - Prob. 91ECh. 5.5 - Prob. 92ECh. 5.5 - Prob. 93ECh. 5.5 - Prob. 94ECh. 5.5 - Prob. 95ECh. 5.5 - Prob. 96ECh. 5.5 - Prob. 97ECh. 5.5 - Prob. 98ECh. 5.5 - Timber Yield The yield V (in millions of cubic...Ch. 5.5 - Prob. 100ECh. 5.5 - Prob. 101ECh. 5.5 - Modeling Data The breaking strengths B (in tons)...Ch. 5.5 - Prob. 103ECh. 5.5 - Prob. 104ECh. 5.5 - Prob. 105ECh. 5.5 - Prob. 106ECh. 5.5 - Prob. 107ECh. 5.5 - Prob. 108ECh. 5.5 - Prob. 109ECh. 5.5 - Prob. 110ECh. 5.5 - Prob. 111ECh. 5.5 - Prob. 112ECh. 5.5 - Prob. 113ECh. 5.5 - Prob. 114ECh. 5.5 - Tangent Lines (a) Determine y' given yx=xy. (b)...Ch. 5.5 - Prob. 116ECh. 5.5 - Prob. 117ECh. 5.6 - CONCEPT CHECK L' Hopitals Rule Explain the benefit...Ch. 5.6 - Prob. 2ECh. 5.6 - Prob. 3ECh. 5.6 - Prob. 4ECh. 5.6 - Prob. 5ECh. 5.6 - Prob. 6ECh. 5.6 - Prob. 7ECh. 5.6 - Using Two Methods In Exercises 7-14, evaluate the...Ch. 5.6 - Using Two Methods In Exercises 7-14, evaluate the...Ch. 5.6 - Prob. 10ECh. 5.6 - Prob. 11ECh. 5.6 - Prob. 12ECh. 5.6 - Prob. 13ECh. 5.6 - Prob. 14ECh. 5.6 - Prob. 15ECh. 5.6 - Prob. 16ECh. 5.6 - Prob. 17ECh. 5.6 - Prob. 18ECh. 5.6 - Prob. 19ECh. 5.6 - Prob. 20ECh. 5.6 - Prob. 21ECh. 5.6 - Evaluating a Limit In Exercises 15-42, evaluate...Ch. 5.6 - Prob. 23ECh. 5.6 - Prob. 24ECh. 5.6 - Prob. 25ECh. 5.6 - Prob. 26ECh. 5.6 - Prob. 27ECh. 5.6 - Prob. 28ECh. 5.6 - Prob. 29ECh. 5.6 - Evaluating a Limit In Exercises 15-42, evaluate...Ch. 5.6 - Evaluating a Limit In Exercises 15-42, evaluate...Ch. 5.6 - Prob. 32ECh. 5.6 - Prob. 33ECh. 5.6 - Prob. 34ECh. 5.6 - Prob. 35ECh. 5.6 - Prob. 36ECh. 5.6 - Prob. 37ECh. 5.6 - Prob. 38ECh. 5.6 - Prob. 39ECh. 5.6 - Prob. 40ECh. 5.6 - Prob. 41ECh. 5.6 - Prob. 42ECh. 5.6 - Prob. 43ECh. 5.6 - Prob. 44ECh. 5.6 - Prob. 45ECh. 5.6 - Prob. 46ECh. 5.6 - Prob. 47ECh. 5.6 - Evaluating a Limit In Exercises 43-62, (a)...Ch. 5.6 - Prob. 49ECh. 5.6 - Prob. 50ECh. 5.6 - Prob. 51ECh. 5.6 - Prob. 52ECh. 5.6 - Prob. 53ECh. 5.6 - Prob. 54ECh. 5.6 - Prob. 55ECh. 5.6 - Prob. 56ECh. 5.6 - Evaluating a Limit In Exercises 43-62, (a)...Ch. 5.6 - Prob. 58ECh. 5.6 - Prob. 59ECh. 5.6 - Evaluating a Limit In Exercises 43-62, (a)...Ch. 5.6 - Prob. 61ECh. 5.6 - Prob. 62ECh. 5.6 - Prob. 63ECh. 5.6 - Prob. 64ECh. 5.6 - Prob. 65ECh. 5.6 - Prob. 66ECh. 5.6 - Prob. 67ECh. 5.6 - Prob. 68ECh. 5.6 - Prob. 69ECh. 5.6 - Prob. 70ECh. 5.6 - Prob. 71ECh. 5.6 - Prob. 72ECh. 5.6 - Prob. 73ECh. 5.6 - Prob. 74ECh. 5.6 - Prob. 75ECh. 5.6 - Prob. 76ECh. 5.6 - Asymptotes and Relative Extrema In Exercises...Ch. 5.6 - Prob. 78ECh. 5.6 - Prob. 79ECh. 5.6 - Prob. 80ECh. 5.6 - Prob. 81ECh. 5.6 - Prob. 82ECh. 5.6 - Prob. 83ECh. 5.6 - Prob. 84ECh. 5.6 - Prob. 85ECh. 5.6 - Prob. 86ECh. 5.6 - Prob. 87ECh. 5.6 - Prob. 88ECh. 5.6 - Prob. 89ECh. 5.6 - Prob. 90ECh. 5.6 - Prob. 91ECh. 5.6 - Prob. 92ECh. 5.6 - Prob. 93ECh. 5.6 - Prob. 94ECh. 5.6 - Prob. 95ECh. 5.6 - Prob. 96ECh. 5.6 - Prob. 97ECh. 5.6 - Prob. 98ECh. 5.6 - Prob. 99ECh. 5.6 - Prob. 100ECh. 5.6 - Prob. 101ECh. 5.6 - Finding a Limit In Section 1.3, a geometric...Ch. 5.6 - Prob. 103ECh. 5.6 - Prob. 104ECh. 5.6 - Prob. 105ECh. 5.6 - Prob. 106ECh. 5.6 - Prob. 107ECh. 5.6 - Prob. 108ECh. 5.6 - Prob. 109ECh. 5.6 - Prob. 110ECh. 5.6 - Prob. 111ECh. 5.6 - Prob. 112ECh. 5.6 - Prob. 113ECh. 5.6 - Prob. 114ECh. 5.6 - Prob. 115ECh. 5.6 - Prob. 116ECh. 5.6 - Prob. 117ECh. 5.7 - Prob. 1ECh. 5.7 - Restricted Domain What is a restricted domain? Why...Ch. 5.7 - Prob. 3ECh. 5.7 - Prob. 4ECh. 5.7 - Prob. 5ECh. 5.7 - Finding Coordinates In Exercises 5 and 6,...Ch. 5.7 - Prob. 7ECh. 5.7 - Prob. 8ECh. 5.7 - Prob. 9ECh. 5.7 - Prob. 10ECh. 5.7 - Prob. 11ECh. 5.7 - Prob. 12ECh. 5.7 - Prob. 13ECh. 5.7 - Evaluating Inverse Trigonometric Functions In...Ch. 5.7 - Approximating Inverse Trigonometric Functions In...Ch. 5.7 - Prob. 16ECh. 5.7 - Prob. 17ECh. 5.7 - Prob. 18ECh. 5.7 - Prob. 19ECh. 5.7 - Prob. 20ECh. 5.7 - Prob. 21ECh. 5.7 - Prob. 22ECh. 5.7 - Prob. 23ECh. 5.7 - Prob. 24ECh. 5.7 - Evaluating an Expression In Exercises 25-28,...Ch. 5.7 - Prob. 26ECh. 5.7 - Prob. 27ECh. 5.7 - Prob. 28ECh. 5.7 - Simplifying an Expression Using a Right Triangle...Ch. 5.7 - Prob. 30ECh. 5.7 - Prob. 31ECh. 5.7 - Prob. 32ECh. 5.7 - Prob. 33ECh. 5.7 - Simplifying an Expression Using a Right Triangle...Ch. 5.7 - Prob. 35ECh. 5.7 - Prob. 36ECh. 5.7 - Prob. 37ECh. 5.7 - Prob. 38ECh. 5.7 - Prob. 39ECh. 5.7 - Prob. 40ECh. 5.7 - Prob. 41ECh. 5.7 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.7 - Prob. 43ECh. 5.7 - Prob. 44ECh. 5.7 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.7 - Prob. 46ECh. 5.7 - Prob. 47ECh. 5.7 - Prob. 48ECh. 5.7 - Prob. 49ECh. 5.7 - Prob. 50ECh. 5.7 - Prob. 51ECh. 5.7 - Prob. 52ECh. 5.7 - Prob. 53ECh. 5.7 - Prob. 54ECh. 5.7 - Prob. 55ECh. 5.7 - Prob. 56ECh. 5.7 - Prob. 57ECh. 5.7 - Prob. 58ECh. 5.7 - Prob. 59ECh. 5.7 - Prob. 60ECh. 5.7 - Prob. 61ECh. 5.7 - Prob. 62ECh. 5.7 - Prob. 63ECh. 5.7 - Prob. 64ECh. 5.7 - Prob. 65ECh. 5.7 - Prob. 66ECh. 5.7 - Analyzing an Inverse Trigonometric Graph In...Ch. 5.7 - Prob. 68ECh. 5.7 - Prob. 69ECh. 5.7 - Prob. 70ECh. 5.7 - Prob. 71ECh. 5.7 - Prob. 72ECh. 5.7 - Prob. 73ECh. 5.7 - Prob. 74ECh. 5.7 - Prob. 75ECh. 5.7 - Prob. 76ECh. 5.7 - Prob. 77ECh. 5.7 - Prob. 78ECh. 5.7 - Prob. 79ECh. 5.7 - Prob. 80ECh. 5.7 - Verifying Identities In Exercises 81 and 82,...Ch. 5.7 - Prob. 82ECh. 5.7 - Prob. 83ECh. 5.7 - Prob. 84ECh. 5.7 - Prob. 85ECh. 5.7 - Prob. 86ECh. 5.7 - Angular Rate of Change An airplane flies at an...Ch. 5.7 - Prob. 88ECh. 5.7 - Angular Rate of Change In a free-fall experiment,...Ch. 5.7 - Prob. 90ECh. 5.7 - Prob. 91ECh. 5.7 - Angular Speed A patrol car is parked 50 feet from...Ch. 5.7 - Proof (a) Prove that...Ch. 5.7 - Prob. 94ECh. 5.7 - Prob. 95ECh. 5.7 - Think About It Use a graphing utility to graph...Ch. 5.7 - Maximizing an Angle In the figure, find the value...Ch. 5.7 - Prob. 98ECh. 5.7 - Prob. 99ECh. 5.7 - Prob. 100ECh. 5.8 - Prob. 1ECh. 5.8 - Prob. 2ECh. 5.8 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.8 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.8 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.8 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.8 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.8 - Prob. 8ECh. 5.8 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.8 - Prob. 10ECh. 5.8 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.8 - Prob. 12ECh. 5.8 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.8 - Prob. 14ECh. 5.8 - Prob. 15ECh. 5.8 - Prob. 16ECh. 5.8 - Prob. 17ECh. 5.8 - Prob. 18ECh. 5.8 - Prob. 19ECh. 5.8 - Prob. 20ECh. 5.8 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.8 - Prob. 22ECh. 5.8 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.8 - Prob. 24ECh. 5.8 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.8 - Prob. 26ECh. 5.8 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.8 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.8 - Prob. 29ECh. 5.8 - Prob. 30ECh. 5.8 - Prob. 31ECh. 5.8 - Prob. 32ECh. 5.8 - Prob. 33ECh. 5.8 - Prob. 34ECh. 5.8 - Completing the Square In Exercises 35-42, find or...Ch. 5.8 - Prob. 36ECh. 5.8 - Completing the Square In Exercises 35-42, find or...Ch. 5.8 - Prob. 38ECh. 5.8 - Prob. 39ECh. 5.8 - Prob. 40ECh. 5.8 - Prob. 41ECh. 5.8 - Prob. 42ECh. 5.8 - Prob. 43ECh. 5.8 - Prob. 44ECh. 5.8 - Prob. 45ECh. 5.8 - Prob. 46ECh. 5.8 - Prob. 47ECh. 5.8 - Prob. 48ECh. 5.8 - Prob. 49ECh. 5.8 - Prob. 50ECh. 5.8 - Prob. 51ECh. 5.8 - Prob. 52ECh. 5.8 - Prob. 53ECh. 5.8 - Prob. 54ECh. 5.8 - Prob. 55ECh. 5.8 - Prob. 56ECh. 5.8 - Prob. 57ECh. 5.8 - Prob. 58ECh. 5.8 - Prob. 59ECh. 5.8 - Prob. 60ECh. 5.8 - Prob. 61ECh. 5.8 - Prob. 62ECh. 5.8 - Prob. 63ECh. 5.8 - Prob. 64ECh. 5.8 - Prob. 65ECh. 5.8 - Prob. 66ECh. 5.8 - Prob. 67ECh. 5.8 - Prob. 68ECh. 5.8 - Prob. 69ECh. 5.8 - Prob. 70ECh. 5.8 - Prob. 71ECh. 5.8 - Prob. 72ECh. 5.8 - Prob. 73ECh. 5.8 - Prob. 74ECh. 5.8 - Prob. 75ECh. 5.8 - Prob. 76ECh. 5.8 - Prob. 77ECh. 5.8 - Prob. 78ECh. 5.9 - Prob. 1ECh. 5.9 - Prob. 2ECh. 5.9 - CONCEPT CHECK Hyperbolic Identities Which...Ch. 5.9 - Prob. 4ECh. 5.9 - Prob. 5ECh. 5.9 - Evaluating a Function In Exercises 5-10, evaluate...Ch. 5.9 - Prob. 7ECh. 5.9 - Prob. 8ECh. 5.9 - Prob. 9ECh. 5.9 - Prob. 10ECh. 5.9 - Prob. 11ECh. 5.9 - Prob. 12ECh. 5.9 - Verifying an Identity In Exercises 11-18, verify...Ch. 5.9 - Prob. 14ECh. 5.9 - Prob. 15ECh. 5.9 - Prob. 16ECh. 5.9 - Prob. 17ECh. 5.9 - Prob. 18ECh. 5.9 - Prob. 19ECh. 5.9 - Prob. 20ECh. 5.9 - Prob. 21ECh. 5.9 - Prob. 22ECh. 5.9 - Prob. 23ECh. 5.9 - Prob. 24ECh. 5.9 - Prob. 25ECh. 5.9 - Prob. 26ECh. 5.9 - Prob. 27ECh. 5.9 - Prob. 28ECh. 5.9 - Prob. 29ECh. 5.9 - Prob. 30ECh. 5.9 - Prob. 31ECh. 5.9 - Finding a Derivative In Exercises 25-34, find the...Ch. 5.9 - Prob. 33ECh. 5.9 - Prob. 34ECh. 5.9 - Prob. 35ECh. 5.9 - Prob. 36ECh. 5.9 - Prob. 37ECh. 5.9 - Prob. 38ECh. 5.9 - Finding Relative Extrema In Exercises 39-42, find...Ch. 5.9 - Prob. 40ECh. 5.9 - Prob. 41ECh. 5.9 - Prob. 42ECh. 5.9 - Prob. 43ECh. 5.9 - Catenary In Exercises 43 and 44, a model for a...Ch. 5.9 - Prob. 45ECh. 5.9 - Prob. 46ECh. 5.9 - Prob. 47ECh. 5.9 - Prob. 48ECh. 5.9 - Prob. 49ECh. 5.9 - Prob. 50ECh. 5.9 - Prob. 51ECh. 5.9 - Prob. 52ECh. 5.9 - Prob. 53ECh. 5.9 - Prob. 54ECh. 5.9 - Prob. 55ECh. 5.9 - Prob. 56ECh. 5.9 - Prob. 57ECh. 5.9 - Prob. 58ECh. 5.9 - Prob. 59ECh. 5.9 - Prob. 60ECh. 5.9 - Prob. 61ECh. 5.9 - Prob. 62ECh. 5.9 - Prob. 63ECh. 5.9 - Prob. 64ECh. 5.9 - Prob. 65ECh. 5.9 - Prob. 66ECh. 5.9 - Prob. 67ECh. 5.9 - Prob. 68ECh. 5.9 - Prob. 69ECh. 5.9 - Prob. 70ECh. 5.9 - Prob. 71ECh. 5.9 - Prob. 72ECh. 5.9 - Prob. 73ECh. 5.9 - Prob. 74ECh. 5.9 - Prob. 75ECh. 5.9 - Prob. 76ECh. 5.9 - Prob. 77ECh. 5.9 - Prob. 78ECh. 5.9 - Prob. 79ECh. 5.9 - Prob. 80ECh. 5.9 - Prob. 81ECh. 5.9 - Prob. 82ECh. 5.9 - Prob. 83ECh. 5.9 - Prob. 84ECh. 5.9 - Prob. 85ECh. 5.9 - Prob. 86ECh. 5.9 - Prob. 87ECh. 5.9 - Prob. 88ECh. 5.9 - Prob. 89ECh. 5.9 - Prob. 90ECh. 5.9 - Prob. 91ECh. 5.9 - Prob. 92ECh. 5.9 - Tractrix Consider the equation of a tractrix...Ch. 5.9 - Prob. 94ECh. 5.9 - Prob. 95ECh. 5.9 - Prob. 96ECh. 5.9 - Using a Right Triangle Show that...Ch. 5.9 - Prob. 98ECh. 5.9 - Prob. 99ECh. 5.9 - Prob. 100ECh. 5.9 - Prob. 101ECh. 5.9 - Prob. 102ECh. 5.9 - Prob. 103ECh. 5.9 - Prob. 104ECh. 5.9 - Prob. 105ECh. 5.9 - Prob. 106ECh. 5 - Prob. 1RECh. 5 - Prob. 2RECh. 5 - Prob. 3RECh. 5 - Prob. 4RECh. 5 - Prob. 5RECh. 5 - Prob. 6RECh. 5 - Prob. 7RECh. 5 - Prob. 8RECh. 5 - Prob. 9RECh. 5 - Prob. 10RECh. 5 - Prob. 11RECh. 5 - Prob. 12RECh. 5 - Prob. 13RECh. 5 - Prob. 14RECh. 5 - Prob. 15RECh. 5 - Prob. 16RECh. 5 - Prob. 17RECh. 5 - Prob. 18RECh. 5 - Prob. 19RECh. 5 - Prob. 20RECh. 5 - Prob. 21RECh. 5 - Prob. 22RECh. 5 - Prob. 23RECh. 5 - Prob. 24RECh. 5 - Prob. 25RECh. 5 - Prob. 26RECh. 5 - Prob. 27RECh. 5 - Prob. 28RECh. 5 - Prob. 29RECh. 5 - Prob. 30RECh. 5 - Prob. 31RECh. 5 - Prob. 32RECh. 5 - Prob. 33RECh. 5 - Prob. 34RECh. 5 - Prob. 35RECh. 5 - Prob. 36RECh. 5 - Prob. 37RECh. 5 - Prob. 38RECh. 5 - Evaluating the Derivative of an Inverse Function...Ch. 5 - Prob. 40RECh. 5 - Prob. 41RECh. 5 - Prob. 42RECh. 5 - Prob. 43RECh. 5 - Prob. 44RECh. 5 - Prob. 45RECh. 5 - Prob. 46RECh. 5 - Prob. 47RECh. 5 - Prob. 48RECh. 5 - Prob. 49RECh. 5 - Prob. 50RECh. 5 - Prob. 51RECh. 5 - Prob. 52RECh. 5 - Prob. 53RECh. 5 - Prob. 54RECh. 5 - Prob. 55RECh. 5 - Prob. 56RECh. 5 - Prob. 57RECh. 5 - Prob. 58RECh. 5 - Prob. 59RECh. 5 - Finding an Indefinite Integral In Exercises 5760,...Ch. 5 - Prob. 61RECh. 5 - Prob. 62RECh. 5 - Prob. 63RECh. 5 - Prob. 64RECh. 5 - Prob. 65RECh. 5 - Prob. 66RECh. 5 - Prob. 67RECh. 5 - Prob. 68RECh. 5 - Prob. 69RECh. 5 - Prob. 70RECh. 5 - Prob. 71RECh. 5 - Prob. 72RECh. 5 - Prob. 73RECh. 5 - Prob. 74RECh. 5 - Prob. 75RECh. 5 - Prob. 76RECh. 5 - Prob. 77RECh. 5 - Prob. 78RECh. 5 - Prob. 79RECh. 5 - Prob. 80RECh. 5 - Prob. 81RECh. 5 - Prob. 82RECh. 5 - Prob. 83RECh. 5 - Prob. 84RECh. 5 - Prob. 85RECh. 5 - Prob. 86RECh. 5 - Prob. 87RECh. 5 - Prob. 88RECh. 5 - Prob. 89RECh. 5 - Prob. 90RECh. 5 - Prob. 91RECh. 5 - Prob. 92RECh. 5 - Prob. 93RECh. 5 - Prob. 94RECh. 5 - Evaluating a Limit In Exercises 8996, use LHpitals...Ch. 5 - Prob. 96RECh. 5 - Evaluating an Expression In Exercises 97 and 98,...Ch. 5 - Prob. 98RECh. 5 - Prob. 99RECh. 5 - Prob. 100RECh. 5 - Prob. 101RECh. 5 - Prob. 102RECh. 5 - Prob. 103RECh. 5 - Finding a Derivative In Exercises 99-104, find the...Ch. 5 - Prob. 105RECh. 5 - Prob. 106RECh. 5 - Prob. 107RECh. 5 - Prob. 108RECh. 5 - Prob. 109RECh. 5 - Prob. 110RECh. 5 - Prob. 111RECh. 5 - Prob. 112RECh. 5 - Prob. 113RECh. 5 - Prob. 114RECh. 5 - Prob. 115RECh. 5 - Area In Exercises 115 and 116, find the area of...Ch. 5 - Prob. 117RECh. 5 - Prob. 118RECh. 5 - Prob. 119RECh. 5 - Prob. 120RECh. 5 - Prob. 121RECh. 5 - Prob. 122RECh. 5 - Prob. 123RECh. 5 - Prob. 124RECh. 5 - Prob. 125RECh. 5 - Prob. 126RECh. 5 - Prob. 127RECh. 5 - Prob. 128RECh. 5 - Prob. 129RECh. 5 - Prob. 130RECh. 5 - Prob. 131RECh. 5 - Prob. 132RECh. 5 - Prob. 133RECh. 5 - Prob. 134RECh. 5 - Prob. 1PSCh. 5 - Prob. 2PSCh. 5 - Prob. 3PSCh. 5 - Prob. 4PSCh. 5 - Finding Limits Use a graphing utility to estimate...Ch. 5 - Prob. 6PSCh. 5 - Prob. 7PSCh. 5 - Prob. 8PSCh. 5 - Area Consider the three regions A, B, and C...Ch. 5 - Prob. 10PSCh. 5 - Prob. 11PSCh. 5 - Prob. 12PSCh. 5 - Prob. 13PSCh. 5 - Prob. 14PSCh. 5 - Prob. 15PSCh. 5 - Mortgage A $120,000 home mortgage for 35 years at...Ch. 5 - Prob. 17PS
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- 1 R2 X2 2) slots per pole per phase = 3/31 B = 180 - 60 msl Kd Kol, Sin (no) Isin (6) 2 sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed; 120*50 Looo rem G S = 1000-950 solos 1000 Copper losses: 5kw Rotor input: 5 loo kw 0.05 1 اذا میرید شرح الكتب فقط look 7) rotor DC ined sove in pea PU+96er Q2// Find the volume of the solid bounded above by the cynnuer 2=6-x², on the sides by the cylinder x² + y² = 9, and below by the xy-plane. Q041 Convert 2 2x-2 Lake Gex 35 w2x-xབོ ,4-ཙཱཔ-y √4-x²-yz 21xy²dzdydx to(a) cylindrical coordinates, (b) Spherical coordinates. 201 25arrow_forwardshow full work pleasearrow_forward3. Describe the steps you would take to find the absolute max of the following function using Calculus f(x) = : , [-1,2]. Then use a graphing calculator to x-1 x²-x+1 approximate the absolute max in the closed interval.arrow_forward
- (7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz). Ꮖ (a) (4 points) Show that V x F = 0. (b) (4 points) Find a potential f for the vector field F. (c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use Stokes' Theorem to calculate the line integral Jos F.ds; as denotes the boundary of S. Explain your answer.arrow_forward(3) (16 points) Consider z = uv, u = x+y, v=x-y. (a) (4 points) Express z in the form z = fog where g: R² R² and f: R² → R. (b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate steps otherwise no credit. (c) (4 points) Let S be the surface parametrized by T(x, y) = (x, y, ƒ (g(x, y)) (x, y) = R². Give a parametric description of the tangent plane to S at the point p = T(x, y). (d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic approximation) of F = (fog) at a point (a, b). Verify that Q(x,y) F(a+x,b+y). =arrow_forward(6) (8 points) Change the order of integration and evaluate (z +4ry)drdy . So S√ ² 0arrow_forward
- (10) (16 points) Let R>0. Consider the truncated sphere S given as x² + y² + (z = √15R)² = R², z ≥0. where F(x, y, z) = −yi + xj . (a) (8 points) Consider the vector field V (x, y, z) = (▼ × F)(x, y, z) Think of S as a hot-air balloon where the vector field V is the velocity vector field measuring the hot gasses escaping through the porous surface S. The flux of V across S gives the volume flow rate of the gasses through S. Calculate this flux. Hint: Parametrize the boundary OS. Then use Stokes' Theorem. (b) (8 points) Calculate the surface area of the balloon. To calculate the surface area, do the following: Translate the balloon surface S by the vector (-15)k. The translated surface, call it S+ is part of the sphere x² + y²+z² = R². Why do S and S+ have the same area? ⚫ Calculate the area of S+. What is the natural spherical parametrization of S+?arrow_forward(1) (8 points) Let c(t) = (et, et sint, et cost). Reparametrize c as a unit speed curve starting from the point (1,0,1).arrow_forward(9) (16 points) Let F(x, y, z) = (x² + y − 4)i + 3xyj + (2x2 +z²)k = - = (x²+y4,3xy, 2x2 + 2²). (a) (4 points) Calculate the divergence and curl of F. (b) (6 points) Find the flux of V x F across the surface S given by x² + y²+2² = 16, z ≥ 0. (c) (6 points) Find the flux of F across the boundary of the unit cube E = [0,1] × [0,1] x [0,1].arrow_forward
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