| ^ | When x + 0 Check the saturation of the following observer at the point x = 0: (x) = {x 0, when x = 0

Show that the following function is continuous at x = 0: f(x) = x sin1.x, when x ne 0 f(0) = 0.

Show that the following function are continuous at x=0: f(x) = {:{(xcos(1/x), when x ne0),(0,whenx=0):}

sgn(x)=(|x|)/(x)=0 when x=0

Given, f (x) = x when x ge 0 = - x , when x lt 0

Examine whether the following function is continuous at x = 0 . phi(x) = {:[|x|/x, when ,x ne 0],[0,when ,x = 0]:}

Examine the continuity of the following function at x = 0 : phi(x)={{:(|2x|/(x)," when " xne0),(0,"when " x=0):}

Check the continuity of the following functions: f(x){(1)/(1-e^((1)/(x))),x!=0 and 0,x=0

Examine the continuity of the function f(x) at x = 0. f(x)={{:(sinx/x" when "xne0),(2" when "x = 0):}

Show that the following functions are continuous at x = 0 : f(x)={{:(x"cos"1/x" when "xne0),(0" when "x=0):}

In the following, determine the constant so that given function is continuous at indicated point: f(x) ={:{((sin2x)/(5x), when x ne0),(m, when x=0):} at x =0