A community for students.
Here's the question you clicked on:
 0 viewing
Callisto
 4 years ago
If \(\lim_{x \rightarrow 0^{+}} f(x)=A\) and \(\lim_{x \rightarrow 0^{}} f(x)=B\), find \(\lim_{x \rightarrow 0^{+}} f(x^3x)\)
How to start?
Callisto
 4 years ago
If \(\lim_{x \rightarrow 0^{+}} f(x)=A\) and \(\lim_{x \rightarrow 0^{}} f(x)=B\), find \(\lim_{x \rightarrow 0^{+}} f(x^3x)\) How to start?

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0hmmm maybe find out whether \(x^3x\) is approaching 0 from the right or the left as x approaches 0 from the right

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0How....? FYI, I have the answer :\

slaaibak
 4 years ago
Best ResponseYou've already chosen the best response.0What's the answer? lol

slaaibak
 4 years ago
Best ResponseYou've already chosen the best response.0When in doubt, go with DNE, lol

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0you can reason as follows: for small positive values of \(x\) we have \(x^3<x\) and so \(x^3x<0\)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0this is my best guess at any rate i am trying to think up a counter example, one where you wouldn't know the limit, but off the top of my head i cannot, so perhaps what i wrote is correct

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0in english, as \(x\to 0^+\) we have \(x^3x\to 0^\)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so my guess is \(B\) although i have a 50% chance of being right even if my reasoning is faulty

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0Assuming your way to do this question is correct. Similarly, for the question (in part b) \(\lim_{x \rightarrow 0^{}} f(x^3x)\) \[x^3x>0\]So, as \(x \rightarrow 0^+\), \(x^3x \rightarrow 0^{+}\). And it is A. Hmmm...

UnkleRhaukus
 4 years ago
Best ResponseYou've already chosen the best response.0is the limit of the function of a sum , equal to the sum of the limits of the function ?

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0As for part c, \[\lim_{x \rightarrow 0^{+}} f(x^2x^4)\] \[x^2x^4>0\] As \(x \rightarrow 0^{+}\), \(x^2x^4\rightarrow 0^{+}\), so it is A. Seems this trick works, but I don't know why...

HELP!!!!
 4 years ago
Best ResponseYou've already chosen the best response.0teach me how to do this
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.