[" Is "f(x)=(1+x)^(x)," when "x!=0],[=e,quad " when "x=0]

Is f(x)=(1+x)^((1)/(x)), when x!=0=e, when x=0 continuous at x=0?

Show that the function f(x) given by f(x)={(e^(1/x)-1)/(e^(1/x)+1), when x!=00,quad when x=0 is discontinuous at x=0

If f(x)={(sin3x)/(x), when x!=01,quad when x=0. Find whether f(x) is continuous at x=0

If the function f(x)={{:((1-cos(ax))/(x^2)," when "xne0),(1," when "x=0):} be continuous at x=0, then find the value of a.

A function f(x) is defined as f(x)= {:{(1," when " x != 0),(2," when " x = 0 ):} does the Limit of f(x) as x to 0 exist ? Explain your answer .

test the continuity of function at x=0f(x)={(1)/(1+2^((1)/(x))), when x!=0,1 when x=0}

Show that the function f(x) given by f(x)={((e^(1/x)-1)/(e^(1/x)+1), when x!=0), (0, when x=0):} is discontinuous at x=0 .

If f(x)={(x"sin"(1)/(x),"when "x ne 0),(0,"when "x =0):} then at x = 0, the function f(x) is -

If f(x)={{:((|sinx|)/(x),"when "xne0),(1,"when "x=0):} then examine the continuity of the function at x = 0.

Test the continuity of the function f (x) : f(x)={{:(x^(2)sin.(1)/(x),"when " xne0),(0,"when " x=0):}