(adsbygoogle = window.adsbygoogle || []).push({}); 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!

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# Homework Help: Proofs on Limit and Derivatives

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