A community for students.
Here's the question you clicked on:
 0 viewing
math456
 3 years ago
Help.. Prove that lim as x approaches to 0. x^4cos(2/x)=0
math456
 3 years ago
Help.. Prove that lim as x approaches to 0. x^4cos(2/x)=0

This Question is Closed

Mikael
 3 years ago
Best ResponseYou've already chosen the best response.0Look ziz iz a seempl applicashion of limit lohz:dw:1347737182410:dw

Mikael
 3 years ago
Best ResponseYou've already chosen the best response.0Now , since \[\lim_{x \rightarrow 0} \cos(x) = 1\]

Mikael
 3 years ago
Best ResponseYou've already chosen the best response.0And, on the other hand \[\lim_{x \rightarrow 0} x^4 = 0\]

Mikael
 3 years ago
Best ResponseYou've already chosen the best response.0You have the product of those two being (surprise , surprise !) 0

Mikael
 3 years ago
Best ResponseYou've already chosen the best response.0Ahh sorry it is 2/x so here is the correct solution:

Mikael
 3 years ago
Best ResponseYou've already chosen the best response.0Theorem we all can use states that Product of a Bounded function by another function that tends to zero  also tends to ZERO in the same limit

RaphaelFilgueiras
 3 years ago
Best ResponseYou've already chosen the best response.2use squeeze theorem

Mikael
 3 years ago
Best ResponseYou've already chosen the best response.0Buut\[\cos(\frac{2}{x}) \leq 1, alwayz\]

Mikael
 3 years ago
Best ResponseYou've already chosen the best response.0So we do have true the required assumptions: One of the factors (i.e. cos 2/x) is a bounded function while the other factor : x^4 tends to 0 when x>0

RaphaelFilgueiras
 3 years ago
Best ResponseYou've already chosen the best response.2dw:1347737519682: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.