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Solution: Slopes of tangent linesa. Find all points where

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

Solution for problem 17RE Chapter 10

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 17RE

Slopes of tangent lines

a. Find all points where the following curves have vertical and horizontal tangent lines.

b. Find the slope of the lines tangent to the curve at the origin (when relevant).

c. Sketch the curve and all the tangent lines identified in parts (a) and (b).

r2 = 2 cos 2θ

Step-by-Step Solution:

Solution 17RE

Step 1:

Given  = 2 cos 2θ

(a) First determine  x  and  y  in terms of   r  and  θ    in order to find    dy/dx

  Recall      x  =  r cos θ    and   y  =  r sin θ     where  = 2 cos 2θ

  So    x  =(2 cos 2 cos θ = 2 cos 2 cos θ

And    y =( 2 cos 2θ) sin θ=       (  Here the parameter is  θ.)

 Calculate the derivative    provided that    ≠  0

   dy/dθ   =  -2 cos 3

 dx/dθ   = 

 So                      

Step 2:

(b)Result for horizontal tangents:   

So for  dy/dθ  =  0  =  -2 cos 3

 yields 

Substitute values in r =we get,

Hence the curve has horizontal tangents at the points are

  Result for vertical tangents:  

So for dx/dθ  =  0   

 yields    

Now substituting the initial values of , for each approximate form of we get

Substitute values in we get,

Hence the curve has horizontal tangents at the points are

(,

Step 3 of 4

Chapter 10, Problem 17RE is Solved
Step 4 of 4

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The full step-by-step solution to problem: 17RE from chapter: 10 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The answer to “Slopes of tangent linesa. Find all points where the following curves have vertical and horizontal tangent lines.b. Find the slope of the lines tangent to the curve at the origin (when relevant).c. Sketch the curve and all the tangent lines identified in parts (a) and (b).r2 = 2 cos 2?” is broken down into a number of easy to follow steps, and 50 words. This full solution covers the following key subjects: Lines, Tangent, curve, Find, parts. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Since the solution to 17RE from 10 chapter was answered, more than 267 students have viewed the full step-by-step answer.

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