- #1

Jarfi

- 384

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**How do I find a limit with two variables?**

## Homework Statement

lim(x->0)((1+ax)^(1/3)/(xln(1+x))-(arctan(bx)/(x^3))

http://www.wolframalpha.com/input/?i=lim%28x-%3E0%29%28%281%2Bax%29^%281%2F3%29%2F%28xln%281%2Bx%29%29-%28arctan%28bx%29%2F%28x^3%29%29

I understand that since the denominator x^3ln(1+x)---> 0 then the counter must also go to zero.

But what I do not understand is that since the counter has TWO variables, I always get a function of those two, instead of a solution of each.

The answer in WA isn't even sensible eitherUPDATE:

I have figured some of it, found out that

a= -3/2 and b= 1

Now how do I find the limit?

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