×
Log in to StudySoup
Get Full Access to Calculus - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Calculus - Textbook Survival Guide

What do the limits and have to do with the derivatives of

University Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321717399 | Authors: Joel R. Hass; Maurice D. Weir; George B. Thomas Jr. ISBN: 9780321717399 65

Solution for problem 17E Chapter 3.R

University Calculus: Early Transcendentals | 2nd Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
University Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321717399 | Authors: Joel R. Hass; Maurice D. Weir; George B. Thomas Jr.

University Calculus: Early Transcendentals | 2nd Edition

4 5 1 236 Reviews
27
4
Problem 17E

What do the limits  and  have to do with the derivatives of the sine and cosine functions? What are the derivatives of these functions?

Step-by-Step Solution:

Step 1 of 3:

In this problem, we need to explain what do the limits  have to do with the derivatives of the sine and cosine functions and we have to find the derivatives of these functions.

Step 2 of 3:

We know that those limits are directly used in calculating the derivatives of sin x and cos x.

So, we firstly solve the derivative of sin x

                                             

If we denote  we can write

…………..(1)

Now we solve  

Clearly if we put the limit then we get indeterminate form.

So, we apply L-Hospital Rule

Then, we get

And

From equation (1)

   for any real

Step 3 of 3

Chapter 3.R, Problem 17E is Solved
Textbook: University Calculus: Early Transcendentals
Edition: 2
Author: Joel R. Hass; Maurice D. Weir; George B. Thomas Jr.
ISBN: 9780321717399

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

What do the limits and have to do with the derivatives of

×
Log in to StudySoup
Get Full Access to Calculus - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Calculus - Textbook Survival Guide
×
Reset your password