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Answer: Derivatives Consider the following parametric

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

Solution for problem 47E Chapter 10.1

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 47E

Problem 47E

Derivatives Consider the following parametric curves.

a. Determine dy/dx in terms of t and evaluate it at the given value of t.

b. Make a sketch of the curve showing the tangent line at the point corresponding to the given value of t.

x = cos t, y = 8 sin t; t = π/2

Step-by-Step Solution:

Solution 47E
Step 1:

To obtain the derivative we need which we can also write as

Evaluating
andseparately, we get


   


   

Putting the values
and  into evaluate , we get

.
Hence the value of is .

 at  is  which means the tangent at this point is a horizontal line.  

Step 2 of 2

Chapter 10.1, Problem 47E is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Answer: Derivatives Consider the following parametric