A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Find the limit:
lim as x approaches 0 of cos(1/x)
anonymous
 one year ago
Find the limit: lim as x approaches 0 of cos(1/x)

This Question is Open

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}\cos\left(\frac{1}{x}\right)}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1That, does not exist

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@pgpilot326 can you explain?

Zale101
 one year ago
Best ResponseYou've already chosen the best response.0If you sub in x=0, you'll get a 0 in the denominator which is undefined.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}\cos\left(\frac{1}{x}\right)}=\cos\left(\displaystyle \lim_{x \rightarrow ~0}\frac{1}{x}\right)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0as x approaches 0, 1/x approaches infinity. cos will cycles through all of it's values and not settle on a single value (which it would need to do in order for the limit to exist)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, that is equivalent of \(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}\cos\left(\frac{1}{x}\right)}=\cos\left(\displaystyle \lim_{x \rightarrow ~0}\frac{1}{x}\right)=\cos\left(\displaystyle \lim_{x \rightarrow ~\infty }x\right)\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So it will alternate between 1 and 1

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441658924817:dw
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.