Examine the continuity of the function `'f' at x = 4, if `f(x) ={(|x-4|/(x-4)),(1):}, ((x ne 4),(x =4))`

Examine the continuity of the function 'f' at x = 3, if f(x) ={(|x-3|/(x-3)),(1):}, ((x ne 3),(x =3))

Examine the continuity of the function 'f' at x = 2, if f(x) ={(|x-2|/(x-2)),(1):}, ((x ne 2),(x =2))

Examine the continuity of the function 'f' at x = 0, if f(x) ={(x cos(1/x)),(0):}, ((x ne 0),(x = 0))

Examine the continuity of the function 'f' at x = 0, if f(x) ={(x sin(1/x)),(0):}, ((x ne 0),(x = 0))

Examine the continuity of the function 'f' at x = 0, if f(x) ={(x^2sin(1/x)),(0):}, ((x ne 0),(x = 0))

Examine the continuity of the function f(x) at x = 0, f(x) = {:{(|sinx|/x, when x ne 0),(1, when x=0):}

Examine the continuity of the function: f(x) = {:((x-4)/(2(x-4)), if x ne4),(0, if x =4):} at x =4

Examine the continuity of the function f(x) = {:{(3x-2,xle0),(x+1,x>0):} at x = 0

Examine the continuity of the following function at x = 2 : f(x) = {{:(3x + 1 "," ,x le 2),(4x - 1",", x gt 2):}

Examine the continuity of the function f(x) = {:{(x+1,xle2),(2x-1,x>2):} at x = 2