" Find the limit of "f(x)=(1)/(1+e^(1/x))" at "x=0

The limit of x sin((1)/(e^(x))) as x rarr 0

The limit of x sin (e^(-1//x)) as x rarr0

Discuss the continulity of f(x) = (e^(1/x) -1)/(e^(1/x) + 1) , x ne 0 and f(0) = 0 at x = 0 .

For x>0, let f(x)=int_(1)^(x)(log t)/(1+t)dt. Find the function f(x)+f((1)/(x)) and find the value of f(e)+f((1)/(e))

Discuss the continuity of f ( x ) = (e^(1)/(x)-1)/(e^(1)/(x)+1), x ne 0 and f(0) = 0 at x=0

Find limit lim (x->0) (sqrt(1+x)-1)/x

Find the limits lim_ (x to 1) f(x) where f(x)={:{(x^2+2,x ne1),(1,x=1):}

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

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