Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Evaluate each limit (if it exists). Use $L$ Hospital's rule (if appropriate).$$\lim _{x \rightarrow 0} \frac{\ln \cos x}{x}$$

01:11

Mengsha Y.

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 7

L'Hospital's Rule

Derivatives

Campbell University

University of Michigan - Ann Arbor

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:16

Find the limit. Use l'…

01:32

02:08

01:46

06:17

09:16

04:18

01:42

07:03

00:55

Okay. So here what we have is we're wanting to use looked house rule to find the limit. So we have the inverse sine of X over X. So we see um the arc sine of X over X. When we plug in zero, we get 0/0. So that's ended giving us um the indeterminate form. So instead what we have to do is take the derivative of the numerator and the denominator separately. So we're going to get one over the square root of one minus X squared Divided by one. So that's just going to go away. Now if we plug in zero, what we end up getting as a result is one Over the square root of 1 0, which is just one over the square to one, which is just 1/1, which gives us one as the final answer for this particular limit. And that means that even though it looks complicated at first using inverse sine, we can simplify things with local styles rule to find the women

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Find the limit. Use l'Hospital's Rule where appropriate. If there …

03:21

Give the proper trigonometric substitution and find the transformed integral…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.