Question

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it.\\ $\lim_{x \to 0} \frac{e^x + e^{-x} - 2}{e^x - x - 1}$

          Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it.\\
$\lim_{x \to 0} \frac{e^x + e^{-x} - 2}{e^x - x - 1}$
        
Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it.

limx → 0(e^x + e^-x - 2)/(e^x - x - 1)

Added by Robin O.

Close

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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
e+ e-x -2 lim X-0 ex = x = 1
Close icon
Play audio
Feedback
Powered by NumerAI
David Collins Jennifer Stoner
Danielle Fairburn verified

Hast Aggarwal and 87 other subject Calculus 1 / AB 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

*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.

*

Recommended Videos

-
lim-_x-rightarrow-0-frac1xfrac1x-exlefttext-ans-frace2right

$$ \lim _{x \rightarrow 0} \frac{(1+x)^{\frac{1}{x}}-e}{x}\left\{\text { Ans. }-\frac{e}{2}\right\} $$

Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry

leftlim-_x-rightarrow-inftyleftfrac2-x-12-x1rightx-text-ans-frac1eright

$$ \left.\lim _{x \rightarrow \infty}\left(\frac{2 x-1}{2 x+1}\right)^{x} \text { \{ Ans. } \frac{1}{e}\right\} $$

Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry

lim-_x-rightarrow-0-eoperatornamesgn-xlefttext-ans-e-frac1eright

$$ \lim _{x \rightarrow 0} e^{\operatorname{sgn} x}\left\{\text { Ans. } e, \frac{1}{e}\right\} $$

Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry


*

Recommended Textbooks

-
Calculus: Early Transcendentals

Calculus: Early Transcendentals

James Stewart 8th Edition
achievement 1,682 solutions
Calculus: Early Transcendentals

Calculus: Early Transcendentals

William Briggs, Lyle Cochran, Bernard Gillet 3rd Edition
achievement 1,588 solutions
Thomas Calculus

Thomas Calculus

George B. Thomas Jr. 14th Edition
achievement 1,872 solutions

*

Transcript

-
00:01 So here we are given that 1 plus x to the power 1 by x is equal to e to the power log 1 plus x whole divided by x.
00:12 This is equal to e to the power 1 by x and x minus x square by 2 plus x cube by 3 and continuing this way.
00:21 Also 1 plus x to the power 1 by x is equal to e to the power 1 minus x by 2 plus x squared by 3...
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
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