" Let "f(x)={[x^(p)sin(1)/(x),x!=0],[0,x=0]" then "f(x)" is continuous but not differentiable at "x=0" if "

Let f(x)={{:(,x^(n)sin\ (1)/(x),x ne 0),(,0,x=0):} Then f(x) is continuous but not differentiable at x=0 . If

Let f(x)={{:(,x^(n)"sin "(1)/(x),x ne 0),(,0,x=0):} Then f(x) is continuous but not differentiable at x=0. If

Let f(x)={:{(x^nsin.(1)/x,","xne0),(0,","x=0):} , then f(x) is continuous but not differentiable at x = 0, if

Show that the function f (x) = x ^(p) sin ((1)/(x)) x , ne 0, f (0) =0 is continuous but not differentiable at x=0 if 0 lt p le 1.