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Callisto
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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?
 one year ago
 one year ago
Callisto Group Title
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?
 one year ago
 one year ago

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

Callisto Group TitleBest ResponseYou've already chosen the best response.0
How....? FYI, I have the answer :\
 one year ago

slaaibak Group TitleBest ResponseYou've already chosen the best response.0
What's the answer? lol
 one year ago

slaaibak Group TitleBest ResponseYou've already chosen the best response.0
When in doubt, go with DNE, lol
 one year ago

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

satellite73 Group TitleBest ResponseYou've already chosen the best response.3
this 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
 one year ago

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

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

Callisto Group TitleBest ResponseYou've already chosen the best response.0
Nice *guess* :\
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.0
Assuming 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...
 one year ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
is the limit of the function of a sum , equal to the sum of the limits of the function ?
 one year ago

Callisto Group TitleBest ResponseYou've already chosen the best response.0
As 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...
 one year ago

HELP!!!! Group TitleBest ResponseYou've already chosen the best response.0
teach me how to do this
 one year ago
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