(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

the problem is: prove that if lim x-->0 g(x)=0, then lim x-->0 g(x)sin(1/x)=0. it seems simple enough, but certain parts have me wondering.

2. Relevant equations

so i already know that lim x-->0 sin(1/x) is undefined because the function oscillates near 0. i'm not really sure how to incorporate that without just stating it, though. also, how do i show the effect of lim x-->0 g(x)=0? if a limit is undefined, does it not exist?

3. The attempt at a solution

i'm not sure if this is completely erroneous but my tentative solution is the following:

if lim x-->0 g(x)=0, lim x-->0 g(x)sin(1/x) = [lim x-->0 g(x)]*[lim x-->0 sin(1/x)]= 0*lim x-->0 sin(1/x)

since a number times 0 equals 0, it follows that lim x-->0 g(x)sin(1/x) = 0.

please help!

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# Homework Help: I need some help with a proof

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