T O P I C R E V I E W 
Manu 
Posted  04/13/2012 : 21:35:53 f(0) = 0 f(0+) = f(0) = 0 as f(x) = x2 sin(1/x) So, f(x) is continous at x=0. Now, as it is continous, for its differentiability we cant differentiate f(x) and then check for its continuity. So, we have, d/dx (f(x)) for x not equal to 0 as : d/dx (f(x)) = 2x sin(1/x) + x2 cos (1/x) (1/x2) = 2x sin(1/x)  cos(1/x) , for all x not equal to 0. But, for f'(0) it doest not exist, as cos(1/x) does not exist for x=0. Am I correct. Any help would be good. 
1 L A T E S T R E P L I E S (Newest First) 
someguy 
Posted  04/13/2012 : 21:46:02 Hi Manu, to find f'(0), use the definition of a derivative.
f'(0) = limit[x > 0] (f(x)  f(0))/(x  0)
It may help to recall that sin(1/x) is bounded between 1 and 1 for all x not equal to 0. 

