- #1
kingwinner
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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!
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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