Limit of Function: No Limit Found

[Unskilled]

could anyone tell me if this have a limit:
lim ((exp(x)-1-x)^2)/(x^2 - ln(x^2+1)))
x->0

My conclusion is that this doesn't have a limit. Tried everything, this is an problem that i run into.

 

[daveb]

Have you tried applying L'Hospital's?

 

[VietDao29]

could anyone tell me if this have a limit:
lim ((exp(x)-1-x)^2)/(x^2 - ln(x^2+1)))
x->0

My conclusion is that this doesn't have a limit. Tried everything, this is an problem that i run into.

Have you tried using Maclaurin Series to solve this problem? :)
Hint:
The expansion of exp(x) arround x = 0 is:
$$e ^ x = 1 + x + \frac{x ^ 2}{2} + ...$$
The expansion of ln(x + 1) arround x = 0 is:
$$\ln (x + 1) = x - \frac{x ^ 2}{2} + ...$$
So what's the expansion of ln(x² + 1) arround x = 0?
Can you go from here? :)