f(x)=sin((1)/(x))" If "x!=0" and "f(0)=0

If f(x)=x sin((1)/(x)),x!=0 and f(x)=0,x=0 then show that f'(0) does not exist

Let f be defined on R by f(x)=x^(4)sin(1/x) , if x!=0 and f(0)=0 then (a) f'(0) doesn't exist (b) f'(2-) doesn't exist (c) f'' is not continous at x=0 (d) f''(0) exist but f''' is not continuous at x=0

Let f be defined on R by f(x)= x^(4)sin(1/x) , if x!=0 and f(0)=0 then (a) f'(0) doesn't exist (b) f'(2-) doesn't exist (c) f'' is not continous at x=0 (d) f''(0) exist but f'' is not continuous at x=0

The function f(x)=(x-a)"sin"(1)/(x-a) for x!=a and f(a)=0 is :

Show that f(x) = x sin ((1)/(x)), x ne 0 , f(0) = 0 is continuous at x = 0

Show that the functions f (x) = x ^(3) sin ((1)/(x)) for x ne 0, f (0) =0 is differentiable at x =0.