Show that the function f(x) ={`x sin (1/x)` when x!= 0; = 0, when x=0 is continuous butnot differentiable at x =0

Show that the function f(x)={x(sin1)/(x)quad ,quad when x!=00quad when x=0 is continuous but not differentiable at x=0 .

Show that the function f(x) = {:{(x^n sin(1/x), x ne 0),(0, x = 0):} is continuous but not differentiable at x= 0.

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.

Show that the function f(x)={x^(m)sin((1)/(x)),x!=00,quad x=0 is continuous but not differentiable at x=0, if @

Show that the function f(x) ={( (sin x)/x, when x !=0),( 2, when x =0):} is continuous at each point except 0.

Show that the function f(x) defined as f(x)=cos((1)/(x)),x!=0;0,x=0 is continuous at x=0 but not differentiable at x=0..