Question

Evaluate $\lim _{x \rightarrow 0} \frac{1-\cos x}{\sin ^2 x}$. 

   Evaluate $\lim _{x \rightarrow 0} \frac{1-\cos x}{\sin ^2 x}$.
CLP-1 Differential Calculus 1
CLP-1 Differential Calculus 1
Joel Feldman, Andrew… 1st Edition
Chapter 3, Problem 11 ↓
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
Evaluate $\lim _{x \rightarrow 0} \frac{1-\cos x}{\sin ^2 x}$.
Close icon
Play audio
Feedback
Powered by NumerAI
Danielle Fairburn David Collins
Ivan Kochetkov verified

Jason Orozco and 60 other educators are ready to help you.

Ask a new question
*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs
*

Recommended Videos

-
evaluate-limit-lim-_x-rightarrow-0-frac1-cos-2-xsin-x

Evaluate limit. $$\lim _{x \rightarrow 0^{+}} \frac{1-\cos ^{2} x}{\sin x}$$

Calculus: Early Transcendentals

Limits

Continuity
evaluate-limit-lim-_x-rightarrow-0-fraccos-x-1sin-2-x

Evaluate limit. $$\lim _{x \rightarrow 0} \frac{\cos x-1}{\sin ^{2} x}$$

Calculus: Early Transcendentals

Limits

Continuity
*

Transcript

-
00:01 So we want to evaluate the limit as x goes to 0 plus of 1 minus cosine squared x over sine x.
00:08 And now the numerator should look familiar from your trig identities.
00:15 And we know it's going to be related to sine x.
00:18 So let's go ahead and try to use a trigger identity to rewrite this expression.
00:25 And the one we're going to use is the easiest to remember.
00:31 Sine squared x plus cosine squared x equals one.
00:37 And now we can subtract cosine squared x from both sides to get one minus cosine squared x equals sine squared x.
00:50 And that, of course, is what we have in the numerator there...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade

Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever