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

ISBN: 9780321717399 65

## Solution for problem 17E Chapter 3.R

University Calculus: Early Transcendentals | 2nd Edition

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University Calculus: Early Transcendentals | 2nd Edition

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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

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