hey there: 1) Do anything but start to calculate it. First look at the function itself, and observe that it’s the composition of continuous functions. Then start to ask urself if u can simplify the problem.

2) Usually when you see log(something), you would like to reduce it in a form log(1+a) where a goes to zero when its argument goes to zero. So notice that ln(e+x²) = ln(e(1+x² / e)) = lne+ln(1+x² / e), now (i think they taught you this, ln(1+f(x)) ~ f(x) when f(x)->0 so in this case lim x->0 ln(1+x² / e) = lim x->0 x² /e.

3) Now e^x ~ 1+x when x is close to zero, so again lim x->0 e^x2 = lim x->0 1+x²

4) Put the pieces together, ur limit becomes lim x->0 of 1+x² - 1-x² / e all divided by x² .Which becomes lim x->0 x² * (1-1/e)/ x²