If f(x) = {((1+(4x)/5)^(1/x),x!=0),(e^(4...

If `f(x) = {((1+(4x)/5)^(1/x),x!=0),(e^(4/5),x=0):}`, then

A

(a) `lim_(x to 0) f(x) = e^(2/5)`

B

(b) `lim_(x to 0) f(x)` does not exist

C

(c) f(x) is continuous at x = 0

D

(d) f(x) is discontinuous at x = 0

Verified by Experts

The correct Answer is:

C

Similar Questions

Explore conceptually related problems

If {:(f(x),=((4x+1)/(1-4x))^(1/x),",",x != 0),(,=k, ",",x = 0):} is continuous at x = 0, then k =

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

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

If f (x) = (3x + 4)/( 5x -7), g (x) = (7x +4)/(5x -3) then f [g(x)]=

If f(x) ={((5^(x)-e^(x))/(sin 2x),",",x != 0),(1/2(log 5+1),",",x = 0):} , then

If f(x) = {(x-1,",", x lt 0),(1/4,",",x = 0),(x^2,",",x gt 0):}

The function f(x)={{:(,(e^(1/x)-1)/(e^(1/x)+1),x ne 0),(,0,x=0):}

{:(f(x),=(log(1+kx))/(sin x),",",x != 0),(,=5, ",",x = 0):} If f is continuous at x = 0, then k =

If {:(f(x),=((e^(kx)-1)^(2)sinx)/(x^(3)),",",x != 0),(,=4, ",",x = 0):} is continuous at x = 0, then k =