Show that ` f(x) = (x)/(1 + e^(1//x)), x ne 0 , f(0) = 0 ` is continuous at x = 0

Show that the function f(x)=(x)/(1+e^(1//x),x ne 0, f(0)= 0 is continuous at x = 0

Show that f(x) = x sin ((1)/(x)), x ne 0 , f(0) = 0 is continuous at x = 0

Show that the function f(x) =x sub (1)/(x) , x ne 0 f(0) =0 is continuous at x = 0

Show that the function f(x) = x cos (1//x), x ne 0 f(0) = 1 is discontinuous at x = 0.

Assertion (A) : f(x) = (1)/( 1 + e^(1//e))(x ne 0) " and " f(0) = 0 is right continuous at x = 0 Reason (R) : underset(x to 0+)(Lt ) (1)/(1 + e^(1//x)) = 0 The correct answer is

f(x) - (1- cos (ax))/( x sin x) , x ne 0, f(0) = 1/2 is continuous at x = 0 , a =

f (x) = ((e^(kx)-1)(sin kx))/(4x^(2)) , x ne 0, f(0) = 9 , is continuous at x = 0 , then k =

Find the value of f(0) so that f(x) = (1)/(x) - (2)/(e^(2x) -1) , x ne 0 is continuous at x = 0 .

Show that f(x) = (cos3x - cos4x)/(xsin 2x), x ne 0 , f(0) = (7)/(4) is continuous at x = 0 .

f (x) = (sin x )/(x) , x ne 0 and f(x) is continous at x = 0 then f(0) =