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Callisto
 3 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
 3 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?

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satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3hmmm maybe find out whether \(x^3x\) is approaching 0 from the right or the left as x approaches 0 from the right

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

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

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

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3you can reason as follows: for small positive values of \(x\) we have \(x^3<x\) and so \(x^3x<0\)

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3this 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

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3in english, as \(x\to 0^+\) we have \(x^3x\to 0^\)

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.3so my guess is \(B\) although i have a 50% chance of being right even if my reasoning is faulty

Callisto
 3 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
 3 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
 3 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!!!!
 3 years ago
Best ResponseYou've already chosen the best response.0teach me how to do this
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