I have the function f(x)=x^3/abs(x)(adsbygoogle = window.adsbygoogle || []).push({});

I think that the following are all true:

lim f(x)= inf.

x->inf

lim f(x)= 0

x-> 0+

lim f(x)=0

x-> 0-

lim f(x)= -inf.

x-> -inf

and

lim f(x)= dne.

x-> 0

I'm not sure about the last one, because I thought that ususally when the limit from the left and the limit from the right are the same, this means that the lim does exist at that number (in this case 0)? But I know this function is not defined at x=0.

Now I need to prove while all these limits are what I have claimed them to be. I'm guessing I need to use the def. of continuity but I'm not sure. Please help!

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# Homework Help: Some limit proofs

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