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) ={(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=

Prove that f(x)={x sin((1)/(x)),x!=0,0,x=0 is not 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 the function f(x) defined as f(x)=-(x^(2))/(x),x 0 is continuous but not differentiable at x=0 then find range of n^(2)

Show that the function f(x)={((x^2sin(1/x),if,x!=0),(0,if,x=0)) is differentiable at x=0 and f'(0)=0

If f(x) = {{:(x cos 1/x, x ne 0),(k ,x =0):} is continous at x=0, then

If the function f(x)={[(cos x)^((1)/(x)),x!=0k,x=0k,x=0]} is continuos at x=0 then the value of k]}