(0^((1)/(x)))/(1+e^((1)/(x)))

Examine the continuity of the function f(x) = {((e^((1)/(x)))/(1 + e^((1)/(x)))",","if " x ne 0),(0",","if" x = 0):} at x= 0

lim_(x rarr0+)(xe^((1)/(x)))/(1+e^((1)/(x)))

lim_(x rarr0)(1+e^(-(1)/(x)))/(1-e^(-(1)/(x))))

If f(x)={(e^((1)/(x))/(1+e^((1)/(x)))",", x ne0),(0",",x=0):} , then

Evaluate lim_(x rarr0)(e^((1)/(x))-1)/(e^((1)/(x))+1),x!=0

lim_(x rarr0)(e^((1)/(x))-1)/(e^((1)/(x))+1) is equal to

lim_(x rarr0)(e^((1)/(x))-1)/(e^((1)/(x))+1)

Show that, f(x)= {((e^((1)/(x))-1)/(e^((1)/(x))+1)",",x ne 0),(0",",x=0):} . Is discontinuous at x= 0