If `f ( x) ={(x^(p) cos((1)/(x)),x cancel=0,(0,x=0):}` is differentiable at x=0, then

If f(x)={[(cos x)^((1)/(sin x)),,x!=0],[K,,x=0]} is differentiable at x=0 Then K=

If f(x)={x^(a)cos(1/x),x!=0 and 0, x=0 is differentiable at x=0 then the range of a is

If f(x) = {:{(xsin(1/x),xne0),(0,x=0):} Show that 'f' is not differentiable at x =0

Prove that f(x)={x sin((1)/(x)),x!=0,0,x=0 is not differentiable 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.

Show that the function f(x)={x^(m)sin((1)/(x))0,x!=0,x=0 is differentiable at x=0 if m>1 continuous but not differentiable at x=0, if 0.

If f(x)={{:(x^(p+1)cos.(1)/(x)":", x ne 0),(0":", x=0):} then at x = 0 the function f(x) is