Applied Calculus
7th Edition
ISBN: 9781337514309
Author: Waner
Publisher: Cengage
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Chapter 6.2, Problem 9E
To determine
To calculate: The solution of the integral
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Show that the Laplace equation in Cartesian coordinates:
J²u
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can be reduced to the following form in cylindrical polar coordinates:
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1 8²u
+
Or 7,2 მ)2
= 0.
Find integrating factor
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Chapter 6 Solutions
Applied Calculus
Ch. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - Prob. 10E
Ch. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - Prob. 14ECh. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - Prob. 20ECh. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 6.1 - Prob. 36ECh. 6.1 - Prob. 37ECh. 6.1 - Prob. 38ECh. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - Prob. 42ECh. 6.1 - Find f(x) if f(0)=1 and the tangent line at...Ch. 6.1 - Find f(x) if f(1)=1 and the tangent line at...Ch. 6.1 - Prob. 45ECh. 6.1 - Find f(x) if f(1)=1 and the tangent line at...Ch. 6.1 - Prob. 47ECh. 6.1 - Prob. 48ECh. 6.1 - Marginal Cost The marginal cost of producing the...Ch. 6.1 - Marginal Cost The marginal cost of producing the...Ch. 6.1 - Facebook Membership At the start of 2010, Facebook...Ch. 6.1 - Uploads to YouTube Since YouTube first became...Ch. 6.1 - Median Household Income From 2000 to 2007, median...Ch. 6.1 - Mean Household Income From 2000 to 2007 the mean...Ch. 6.1 - Bottled Water Sales The rate of U.S. sales of...Ch. 6.1 - Bottled Water Sales The rate of U.S. per capita...Ch. 6.1 - Health-Care Spending in the 1990s Write H(t) for...Ch. 6.1 - Health-Care Spending in the 2000s Write H(t) for...Ch. 6.1 - Prob. 59ECh. 6.1 - Subprime Mortgage Debt during the Housing Bubble...Ch. 6.1 - Prob. 61ECh. 6.1 - Prob. 62ECh. 6.1 - Prob. 63ECh. 6.1 - Prob. 64ECh. 6.1 - Prob. 65ECh. 6.1 - Prob. 66ECh. 6.1 - Prob. 67ECh. 6.1 - Prob. 68ECh. 6.1 - Prob. 69ECh. 6.1 - Prob. 70ECh. 6.1 - Prob. 71ECh. 6.1 - Prob. 72ECh. 6.1 - Exercises 7176 use the results of Exercises 69 and...Ch. 6.1 - Prob. 74ECh. 6.1 - Prob. 75ECh. 6.1 - Prob. 76ECh. 6.1 - Prob. 77ECh. 6.1 - Prob. 78ECh. 6.1 - Prob. 79ECh. 6.1 - Prob. 80ECh. 6.1 - Prob. 81ECh. 6.1 - If we know an antiderivative of a function, do we...Ch. 6.1 - Prob. 83ECh. 6.1 - Your friend Marco claims that once you have one...Ch. 6.1 - Prob. 85ECh. 6.1 - Prob. 86ECh. 6.1 - Prob. 87ECh. 6.1 - Prob. 88ECh. 6.1 - Prob. 89ECh. 6.1 - Why was the following marked wrong? What is the...Ch. 6.1 - Prob. 91ECh. 6.1 - Why was the following marked wrong? What is the...Ch. 6.1 - Prob. 93ECh. 6.1 - Prob. 94ECh. 6.1 - Prob. 95ECh. 6.1 - Why was the following marked wrong? What is the...Ch. 6.1 - Prob. 97ECh. 6.1 - Prob. 98ECh. 6.1 - Prob. 99ECh. 6.1 - Prob. 100ECh. 6.1 - Prob. 101ECh. 6.1 - Prob. 102ECh. 6.2 - In Exercises 110, evaluate the given integral...Ch. 6.2 - In Exercises 110, evaluate the given integral...Ch. 6.2 - Prob. 3ECh. 6.2 - Prob. 4ECh. 6.2 - In Exercises 110, evaluate the given integral...Ch. 6.2 - Prob. 6ECh. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - Prob. 9ECh. 6.2 - In Exercises 110, evaluate the given integral...Ch. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 6.2 - In Exercises 1152, decide on what substitution to...Ch. 6.2 - Prob. 15ECh. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Prob. 18ECh. 6.2 - In Exercises 1152, decide on what substitution to...Ch. 6.2 - Prob. 20ECh. 6.2 - Prob. 21ECh. 6.2 - In Exercises 1152, decide on what substitution to...Ch. 6.2 - Prob. 23ECh. 6.2 - Prob. 24ECh. 6.2 - Prob. 25ECh. 6.2 - Prob. 26ECh. 6.2 - Prob. 27ECh. 6.2 - Prob. 28ECh. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Prob. 31ECh. 6.2 - Prob. 32ECh. 6.2 - Prob. 33ECh. 6.2 - Prob. 34ECh. 6.2 - Prob. 35ECh. 6.2 - In Exercises 1152, decide on what substitution to...Ch. 6.2 - Prob. 37ECh. 6.2 - In Exercises 1152, decide on what substitution to...Ch. 6.2 - Prob. 39ECh. 6.2 - Prob. 40ECh. 6.2 - Prob. 41ECh. 6.2 - Prob. 42ECh. 6.2 - Prob. 43ECh. 6.2 - Prob. 44ECh. 6.2 - Prob. 45ECh. 6.2 - Prob. 46ECh. 6.2 - Prob. 47ECh. 6.2 - Prob. 48ECh. 6.2 - Prob. 49ECh. 6.2 - Prob. 50ECh. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Prob. 53ECh. 6.2 - Prob. 54ECh. 6.2 - Prob. 55ECh. 6.2 - Prob. 56ECh. 6.2 - Prob. 57ECh. 6.2 - Prob. 58ECh. 6.2 - Prob. 59ECh. 6.2 - Prob. 60ECh. 6.2 - Prob. 61ECh. 6.2 - Prob. 62ECh. 6.2 - Prob. 63ECh. 6.2 - Prob. 64ECh. 6.2 - Prob. 65ECh. 6.2 - Prob. 66ECh. 6.2 - Prob. 67ECh. 6.2 - Prob. 68ECh. 6.2 - Prob. 69ECh. 6.2 - In Exercises 5772, use the shortcut formulas (see...Ch. 6.2 - Prob. 71ECh. 6.2 - Prob. 72ECh. 6.2 - Prob. 73ECh. 6.2 - Find f(x) if f(1)=0 and the tangent line at...Ch. 6.2 - Prob. 75ECh. 6.2 - Find f(x) if f(2)=1 and the tangent line at x has...Ch. 6.2 - Prob. 77ECh. 6.2 - Prob. 78ECh. 6.2 - Prob. 79ECh. 6.2 - Prob. 80ECh. 6.2 - Prob. 81ECh. 6.2 - In Exercises 7784, use Mikes shortcut method (see...Ch. 6.2 - Prob. 83ECh. 6.2 - Prob. 84ECh. 6.2 - Cost The marginal cost of producing the xth roll...Ch. 6.2 - Prob. 86ECh. 6.2 - Economic Growth The Mexico GDP (total monetary...Ch. 6.2 - Prob. 88ECh. 6.2 - Prob. 89ECh. 6.2 - Revenue: Google The annual revenue of Google Inc....Ch. 6.2 - Scientific Research: 19832003 The number of...Ch. 6.2 - Prob. 92ECh. 6.2 - Prob. 93ECh. 6.2 - Prob. 94ECh. 6.2 - Prob. 95ECh. 6.2 - Motion in a Straight Line The velocity of a...Ch. 6.2 - Bottled Water Sales (Compare Exercise 55 in...Ch. 6.2 - Prob. 98ECh. 6.2 - Prob. 99ECh. 6.2 - You are asked to calculate uu2+1du. What is wrong...Ch. 6.2 - Prob. 101ECh. 6.2 - Prob. 102ECh. 6.2 - Prob. 103ECh. 6.2 - If the substitution u=x21 works in xx21dx, why...Ch. 6.2 - Prob. 105ECh. 6.2 - Why was the following calculation marked wrong?...Ch. 6.2 - Prob. 107ECh. 6.2 - Prob. 108ECh. 6.2 - Prob. 109ECh. 6.2 - Prob. 110ECh. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - Prob. 3ECh. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - Prob. 5ECh. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - In Exercises 1-10, calculate the left Riemann sum...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - In Exercises 11-18, use the given graph to...Ch. 6.3 - Prob. 17ECh. 6.3 - Prob. 18ECh. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - Prob. 22ECh. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - Prob. 25ECh. 6.3 - In Exercises 19-28, use geometry (not Riemann...Ch. 6.3 - Prob. 27ECh. 6.3 - Prob. 28ECh. 6.3 - In Exercises 29-34, the graph of the derivative...Ch. 6.3 - Prob. 30ECh. 6.3 - Prob. 31ECh. 6.3 - In Exercises 29-34, the graph of the derivative...Ch. 6.3 - Prob. 33ECh. 6.3 - In Exercises 29-34, the graph of the derivative...Ch. 6.3 - In Exercises 35-38, use technology to approximate...Ch. 6.3 - Prob. 36ECh. 6.3 - Prob. 37ECh. 6.3 - Prob. 38ECh. 6.3 - Prob. 39ECh. 6.3 - Pumps A pump is delivering water into a tank at a...Ch. 6.3 - Cost The marginal cost function for the...Ch. 6.3 - Prob. 42ECh. 6.3 - Profit: iPhones Assume that Apples marginal cost...Ch. 6.3 - Profit: PlayStation 4s Assume that Sony's marginal...Ch. 6.3 - Bottled Water Sales The rate of U.S. sales of...Ch. 6.3 - Prob. 46ECh. 6.3 - Prob. 47ECh. 6.3 - Online Auctions The following graph shows the rate...Ch. 6.3 - Prob. 49ECh. 6.3 - Scientific Research Exercises 49 and 50 are based...Ch. 6.3 - Graduate Degrees: Women The following graph shows...Ch. 6.3 - Prob. 52ECh. 6.3 - Prob. 53ECh. 6.3 - Prob. 54ECh. 6.3 - Prob. 55ECh. 6.3 - Prob. 56ECh. 6.3 - Prob. 57ECh. 6.3 - Offshore Crude Oil Production: Mexico The...Ch. 6.3 - Prob. 59ECh. 6.3 - Motion under Gravity The velocity of a stone...Ch. 6.3 - Prob. 61ECh. 6.3 - Motion A race car has a velocity given by...Ch. 6.3 - Prob. 63ECh. 6.3 - Uploads to YouTube Since YouTube first became...Ch. 6.3 - Prob. 65ECh. 6.3 - Big Brother The number of wiretaps authorized each...Ch. 6.3 - Surveying My uncle intends to build a...Ch. 6.3 - Pollution An aerial photograph of an ocean oil...Ch. 6.3 - Prob. 69ECh. 6.3 - Prob. 70ECh. 6.3 - The Normal Curve The normal distribution curve,...Ch. 6.3 - The Normal Curve The normal distribution curve,...Ch. 6.3 - Prob. 73ECh. 6.3 - Prob. 74ECh. 6.3 - If f is an increasing function of x, then the left...Ch. 6.3 - If f is a decreasing function of x, then the left...Ch. 6.3 - Prob. 77ECh. 6.3 - Sketch the graphs of two (different) functions f...Ch. 6.3 - Prob. 79ECh. 6.3 - Prob. 80ECh. 6.3 - Prob. 81ECh. 6.3 - Prob. 82ECh. 6.3 - Prob. 83ECh. 6.3 - Prob. 84ECh. 6.3 - Prob. 85ECh. 6.3 - Prob. 86ECh. 6.3 - Prob. 87ECh. 6.3 - Prob. 88ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 15ECh. 6.4 - Prob. 16ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 20ECh. 6.4 - Prob. 21ECh. 6.4 - Prob. 22ECh. 6.4 - Prob. 23ECh. 6.4 - Prob. 24ECh. 6.4 - Prob. 25ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 28ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 30ECh. 6.4 - Prob. 31ECh. 6.4 - Prob. 32ECh. 6.4 - Prob. 33ECh. 6.4 - Prob. 34ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 36ECh. 6.4 - Prob. 37ECh. 6.4 - Prob. 38ECh. 6.4 - Prob. 39ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 41ECh. 6.4 - In Exercises 144, evaluate the integral. [HINT:...Ch. 6.4 - Prob. 43ECh. 6.4 - Prob. 44ECh. 6.4 - Prob. 45ECh. 6.4 - Prob. 46ECh. 6.4 - Prob. 47ECh. 6.4 - Prob. 48ECh. 6.4 - Prob. 49ECh. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - Prob. 51ECh. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - In Exercises 4554, calculate the total area of the...Ch. 6.4 - Prob. 55ECh. 6.4 - Prob. 56ECh. 6.4 - Prob. 57ECh. 6.4 - Prob. 58ECh. 6.4 - Profit: iPhones (Compare Exercise 43 in Section...Ch. 6.4 - Profit: PlayStation 4s (Compare Exercise 44 in...Ch. 6.4 - Prob. 61ECh. 6.4 - Motion A ball thrown in the air has a velocity of...Ch. 6.4 - Prob. 63ECh. 6.4 - Prob. 64ECh. 6.4 - Fuel Consumption The way Professor Waner drives,...Ch. 6.4 - Fuel Consumption The way Professor Costenoble...Ch. 6.4 - Prob. 67ECh. 6.4 - Bottled Water Sales (Compare Exercise 46 in...Ch. 6.4 - Prob. 69ECh. 6.4 - Uploads to YouTube (Compare Exercise 64 in Section...Ch. 6.4 - Big Brother (Compare Exercise 65 in Section 6.3.)...Ch. 6.4 - Big Brother (Compare Exercise 66 in Section 6.3.)...Ch. 6.4 - Prob. 73ECh. 6.4 - Housing Starts: The Great Recession (Compare...Ch. 6.4 - Sales Weekly sales of your Lord of the Rings...Ch. 6.4 - Sales Annual sales of fountain pens in Littleville...Ch. 6.4 - Prob. 77ECh. 6.4 - Embryo Development The oxygen consumption of a...Ch. 6.4 - Prob. 79ECh. 6.4 - Online Auctions The rate of change n(t) of the...Ch. 6.4 - Prob. 81ECh. 6.4 - Cost The total cost of producing x items is given...Ch. 6.4 - Prob. 83ECh. 6.4 - Scientific Research: 19832003 (Compare Exercise 92...Ch. 6.4 - Prob. 85ECh. 6.4 - The Logistic Function and Grant Spending a. Show...Ch. 6.4 - Prob. 87ECh. 6.4 - Prob. 88ECh. 6.4 - Prob. 89ECh. 6.4 - What is definite about the definite integral?Ch. 6.4 - Prob. 91ECh. 6.4 - Prob. 92ECh. 6.4 - Prob. 93ECh. 6.4 - Prob. 94ECh. 6.4 - Prob. 95ECh. 6.4 - Prob. 96ECh. 6.4 - Prob. 97ECh. 6.4 - Explain why, in computing the total change of a...Ch. 6.4 - Prob. 99ECh. 6.4 - Prob. 100ECh. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - Prob. 2RECh. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - Prob. 4RECh. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - Prob. 6RECh. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - Prob. 8RECh. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - Prob. 10RECh. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - Prob. 12RECh. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - Prob. 14RECh. 6 - In Exercises 118, evaluate the indefinite...Ch. 6 - Prob. 16RECh. 6 - Prob. 17RECh. 6 - Prob. 18RECh. 6 - In Exercises 19 and 20, use the given graph to...Ch. 6 - Prob. 20RECh. 6 - In Exercises 2126, calculate the left Riemann sum...Ch. 6 - Prob. 22RECh. 6 - Prob. 23RECh. 6 - Prob. 24RECh. 6 - In Exercises 2126, calculate the left Riemann sum...Ch. 6 - Prob. 26RECh. 6 - In Exercises 27 and 28, use technology to...Ch. 6 - Prob. 28RECh. 6 - Prob. 29RECh. 6 - Prob. 30RECh. 6 - Prob. 31RECh. 6 - Prob. 32RECh. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - Prob. 34RECh. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - Prob. 36RECh. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - Prob. 38RECh. 6 - In Exercises 3140, evaluate the definite integral...Ch. 6 - Prob. 40RECh. 6 - Prob. 41RECh. 6 - Prob. 42RECh. 6 - Prob. 43RECh. 6 - Prob. 44RECh. 6 - Sales At OHaganBooks.com, the rate of net sales...Ch. 6 - Prob. 46RECh. 6 - Motion under Gravity Billy-Sean OHagans friend...Ch. 6 - Prob. 48RECh. 6 - Projected Sales Before OHaganBooks.com launched...Ch. 6 - Prob. 50RECh. 6 - Prob. 51RECh. 6 - Sales The following graph shows the approximate...Ch. 6 - Prob. 53RECh. 6 - Prob. 54RECh. 6 - Prob. 55RECh. 6 - Prob. 56RECh. 6 - Prob. 57RECh. 6 - Prob. 58RECh. 6 - Prob. 59RECh. 6 - Prob. 60RECh. 6 - Prob. 61RECh. 6 - Prob. 62RECh. 6 - Prob. 3CS
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