1) Prove that f defined by f(x)= e^(-1/|x|), x=/=0, f(x)= 0, x=0 is differentiable at 0. [I used the definition of derivative f'(0)=lim [f(0+h)-f(0)] / h = lim [e^(-1/|h|) / h] h->0 h->0 and I am stuck here and unable to proceed...] 2) Suppose lim (x->a) f(x) = L exists and f(x)>0 for all x not =a. Use the definition of limit to prove that L>0. [when I draw a picture, I can see that this is definitely true, but how can I go about proving it?] Thanks for your help!