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

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

f(x)= {((1)/(e^(4x) + 1)",",x ne 0),(0",",x = 0):} Examine the continuity of f(x) at x= 0

Show the function, f(x) = {{:((e^(1//x)-1)/(e^(1//x)+1)",","when",x ne 0),(0",","when",x = 0):} has non-removable discontinuity at x = 0

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

If f(x) = {{:((sin^(-1)x)^(2)cos((1)/(x))",",x ne 0),(0",",x = 0):} then f(x) is

f(x)= {((x(1 + a cos x)-b sin x)/(x^(3))",",x ne 0),(0",",x=0):} . If f is continuous at x=0 then find the value of a and b.

Show that f(x)= {(x^(3)+3",",x ne0),(1",",x=0):} is a discontinuous function at x= 0.

Show that f(x)={{:("x sin"(1)/(x)",","when",x ne 0),(0",","when",x = 0):} is continuous but not differentiable at x = 0

If f(x) = {{:((log(1+2ax)-log(1-bx))/(x)",",x ne 0),(" "k",",x = 0):} is continuous at x = 0, then k is equal to