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The anvil of a hyperbola Let H be the hyperbola x2 y2 = 1

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 98AE Chapter 10.4

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 98AE

Problem 98AE

The anvil of a hyperbola Let H be the hyperbola x2 − y2 = 1 and let S be the 2-by-2 square bisected by the asymptotes of H. Let R be the anvil-shaped region bounded by the hyperbola and the horizontal lines y = ±p (sec figure).

a. For what value of p is the area of R equal to the area of S?

b. For what value of p is the area of R twice the area of S?

Step-by-Step Solution:

Solution 98AE

Step 1:

We find the area of region R by integrating the hyperbola with respect to y from .

Equation of hyperbola in terms of y is :

Now, area is


     
 

 

 


     

Step 2 of 1

Chapter 10.4, Problem 98AE is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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The anvil of a hyperbola Let H be the hyperbola x2 y2 = 1