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How do you find the slope of the line tangent to the polar

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

Solution for problem 2E Chapter 10.3

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 2E

How do you find the slope of the line tangent to the polar graph of r = f(θ) at a point?

Step-by-Step Solution:

Solution 2E

Step 1:

 Consider the following polar equation ;

                              r =  f(

The objective is to find the slope of the line tangent to the given polar graph.

We know that the polar point in cartesian coordinates is x = rcos( , y = r sin(                         

The given polar equation is  r = f(

Therefore , the cartesian coordinates  are  given as ;

         x=  f( , y =  f(sin(.

Hence , the parametric form in cartesian coordinates are ;   x=  f( , y =  f(sin(.

We , know that the slope of the line tangent is ;

So, describing  x and y in terms of  ‘ alone.So , using the chain rule we compute

                                       =  .

Since ,  =  .

Now , we will need the following derivatives.

Consider...

Step 2 of 3

Chapter 10.3, Problem 2E is Solved
Step 3 of 3

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

Since the solution to 2E from 10.3 chapter was answered, more than 259 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: Find, graph, line, point, polar. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The full step-by-step solution to problem: 2E from chapter: 10.3 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. The answer to “How do you find the slope of the line tangent to the polar graph of r = f(?) at a point?” is broken down into a number of easy to follow steps, and 21 words.

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How do you find the slope of the line tangent to the polar