Prove that f (x) =|x| is continuous at x =0

Show that f (x) = |x| is continuous at x= 0 but f'(0) does not exist

Prove that f (x) = [X] is discontinuous for integral values of x.

if f(x+y)=f(x)+ f(y) for all x and y and if f(x) is continuous at x=0, show that f(x) is continuous everywhere.

if f(xy) = f(x) f(y) for all x and y and if f(x) is continuous at x = 1, then show that it is continuous for all x except 0

Prove that f (x) = |x-1|,x in R is not differnentiable at x=1

Show that f (x) = f(x) = {(x,sinfrac(1)(x)),(0,x=0):} is continuous at x = 0

If the function f(x)={{:((sin x)/(x) + cos x", if " x ne 0 ), (k", if " x =0 ):} is continuous at x=0, then find the value of k.

Find the value of k, so that the function f is continuous at the indicated point. f(x)={{:((kappacosx)/(pi-2x)",","if "x ne (pi)/(2),,),(,,,"at " x=(pi)/(2)),(3",", if "x=(pi)/(2),,):}

Prove that f(x) = sin x and f(x) = cos x are continuous.