Determine whether f '(0) exists.

Question

f(x) = {xsin(10/x) if x can not = 0
0 if x=0

Answer 1

consider the function g(x)=sin(10x)/x as x>>inf clearly this has a limit of zero.

Is this not the same function in the limit as f(x)?

Answer 2

You can prove that limx>0 of (f(x)=limx>inf f(1/x)

I should have made that clear.