calculus
posted by Anonymous .
Determine whether f '(0) exists.
f(x) = {xsin(10/x) if x can not = 0
0 if x=0

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)? 
You can prove that limx>0 of (f(x)=limx>inf f(1/x)
I should have made that clear.