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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 10.3 - Problem 2e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 10.3 - Problem 2e

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How do you find the slope of the line tangent to the polar ISBN: 9780321570567 2

Solution for problem 2E Chapter 10.3

Calculus: Early Transcendentals | 1st Edition

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Problem 2E

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 ,    x=  f( , then derivative both sides with respect to ‘ we get ,

= , since (uv) = , and cos(x) = -sin(x).

Consider ,    y =  f( , then derivative both sides with respect to ‘ we get , = , since (uv) = , and sin(x) = cos(x).

Therefore , the slope of the tangent line is; = = .

Step 2 of 1

ISBN: 9780321570567

Since the solution to 2E from 10.3 chapter was answered, more than 333 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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