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 = 4, if f(x) ={(|x-4|/(x-4)),(1):}, ((x ne 4),(x =4))

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) = 2x^2 - 1 at x=3

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

Test the continuity of the function at x = 3 , where f(x) = {{:((|x-3|)/(x(x - 3))"," ,x != 3),(0",", x = 3):}