show that f(x) =|x-2| is continuous but not differentiable at x=2. Please reply!!URGENT!!!

a).|x-2| being a modulus function is continuous

b)For cheking differentiability, at x=2, we need to check if lim h=>0^{+} ( f(2+h) -f(2)/h) should not be equal to lim h=>0^{- }( f(2+h) -f(2)/h) or not

Now, lim h=>0^{+ }f(2+h) -f(2)/h) = lim h=>0^{+} ( !2+h-2! -!2-2! ) /h = lim h=>0^{+} !h! /h = lim h=>0^{+ }h/h =1 (as h= +ve hence !h!=h)

Similarly, lim h=>0^{-} f(2+h) -f(2)/h) = lim h=>0^{-} ( !2+h-2! -!2-2! ) /h = lim h=>0^{-} !h! /h = lim h=>0-^{ -} h/h =-1 (as h= -ve hence !h!= -h)

so lim h=>0^{+} f(2+h) -f(2)/h) is equal to lim h=>0^{-} f(2+h) -f(2)) /h