12th Edition

ISBN: 9781119899761

Author: Anton

Publisher: WILEY

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Textbook Question

Chapter 14.8, Problem 30ES

Find the center of gravity of the cube that is determined by the inequalities 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 , 0 ≤ z ≤ 1 if

(a) the density is proportional to the square of the distance to the origin;

(b) the density is proportional to the sum of the distances to the faces that lie in the coordinate planes.

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Chapter 14.8, Problem 29ES

Chapter 14.8, Problem 31ES

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(b) Find the (instantaneous) rate of change of y at x = 5. In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the following limit. lim h→0 - f(x + h) − f(x) h The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule defining f. f(x + h) = (x + h)² - 5(x+ h) = 2xh+h2_ x² + 2xh + h² 5✔ - 5 )x - 5h Step 4 - The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x). - f(x + h) f(x) = = (x² x² + 2xh + h² - ])- = 2x + h² - 5h ])x-5h) - (x² - 5x) = ]) (2x + h - 5) Macbook Pro

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Let f be defined as follows. y = f(x) = x² - 5x (a) Find the average rate of change of y with respect to x in the following intervals. from x = 4 to x = 5 from x = 4 to x = 4.5 from x = 4 to x = 4.1 (b) Find the (instantaneous) rate of change of y at x = 4. Need Help? Read It Master It

Chapter 14 Solutions

CALCULUS EARLY TRANSCENDENTALS WILEY+

Ch. 14.1 - Prob. 1QCE Ch. 14.1 - The iterated integral 1524fx,ydxdy integrates f...Ch. 14.1 - Supply the missing integrand and limits of...Ch. 14.1 - Prob. 4QCE Ch. 14.1 - Evaluate the iterated integrals. 0102x+3dydx Ch. 14.1 - Evaluate the iterated integrals. 13112x4ydydx Ch. 14.1 - Evaluate the iterated integrals. 2401x2ydxdy Ch. 14.1 - Evaluate the iterated integrals. 2012x2+y2dxdy Ch. 14.1 - Evaluate the iterated integrals. 0ln30ln2ex+ydydx Ch. 14.1 - Prob. 6ES

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