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# Equal volumes Consider the region R bounded by the curves

ISBN: 9780321947345 167

## Solution for problem 63 Chapter 6.4

Calculus: Early Transcendentals | 2nd Edition

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Calculus: Early Transcendentals | 2nd Edition

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Problem 63

Equal volumes Consider the region R bounded by the curves y = ax2 + 1, y = 0, x = 0, and x = 1, for a -1. Let S1 and S2 be solids generated when R is revolved about the x- and y-axes, respectively. a. Find V1 and V2, the volumes of S1 and S2, as functions of a. b. What are the values of a -1 for which V11a2 = V21a2?

Step-by-Step Solution:
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Calculus notes for the week of 10/3/16 4.1 Maxima and Minima and 4.2 What Derivatives Tell Us 15 10 5 01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 -5 -10 -15 f has a local maximum at c if f(c) > f(x) for all x sufficiently close to c. f has a local minimum at c if f(c) < f(x) for all x sufficiently close to c. We see that, if f is differentiable at a local extremum (c), then f’(c) = 0. It is impossible that f is not differentiable at a local extremum. Definition: f has a critical point at x if f ’(x) = 0 or f ’(x) DNE. Coordinates for local extremum will be critical points. We see that, if f ‘(x) is negative on an interval I, then f is decreasing on I. If f ‘(x) is positive on an interval I, then f is

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##### ISBN: 9780321947345

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. The full step-by-step solution to problem: 63 from chapter: 6.4 was answered by , our top Calculus solution expert on 12/23/17, 04:24PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. The answer to “Equal volumes Consider the region R bounded by the curves y = ax2 + 1, y = 0, x = 0, and x = 1, for a -1. Let S1 and S2 be solids generated when R is revolved about the x- and y-axes, respectively. a. Find V1 and V2, the volumes of S1 and S2, as functions of a. b. What are the values of a -1 for which V11a2 = V21a2?” is broken down into a number of easy to follow steps, and 73 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 128 chapters, and 9720 solutions. Since the solution to 63 from 6.4 chapter was answered, more than 239 students have viewed the full step-by-step answer.

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Equal volumes Consider the region R bounded by the curves