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

Show that the function f(x) given by f(x)={(xsin(1/x),x!=0),(0,x=0):} is continuous at x = 0

Show that the function f(x) given by f(x)={(sin x)/(x)+cos x,x!=0 and 2,x=0 is continuous at x=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 function f(x) given by f(x)={(x sin(1/x),,,x ne 0),(0,,,x=0):} is continuous at x=0

Show that the function 'f' defined as follows, is continuous at x = 2, but not differentiable there at: f(x) = {:{(3x-2,0 2):}

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.