Examine the continuity of `f(x) = |x|+|x-2| at x =0 and at x =2`

Examine the continuity of the following function at the given point : f(x) = {(x, 0 le x < 1/2),(1, x = 1/2),(1-x, 1/2 < x < 1):} at x = 1/2 .

Examine the continuity of the following function at the given point : f(x) = {(1 + x, x 0),(1, x = 0):} at x = 0.

Examine the continuity of the following function at the given point : f(x) = {(x^2 - 2x + 3, x 1):} x = 1.

Examine the differentiablity of f at x = 1,2, if f(x)={(x,0ltxlt1),(2x-x^2,1lexle2),(x-x^2/2,xgt2):}

Examine the continuity of the following function at the given point : f(x) ={((3/2-x, 1/2 le x < 1)),((3/2, x = 1)),((3/2 + x, 1 < x le 2)):} at x = 1.

Examine continuity of the function f defined by. f(x) = frac (x^2-25)(x+5)

Examine continuity of the function f defined by. f(x) =|x-5|

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

Examine whether the circles x ^2 + y ^2 - 2x - 4y = 0 and x ^2 + y ^2 - 8y - 4 = 0 touch each other.