Let `f(x)=g(x)(e^(1//x) -e^(-1//x))/(e^(1//x) + e^(-1//x))`, where g is a continuous function then `lim_(x to 0)` f(x) exist if

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

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

Let f(x)=(x)/(1+x^(2)) and g(x)=(e^(-x))/(1+[x]) (where [.] denote greatest integer function), then

f(x)=int_(0)^(x)g(t)log_(e)((1-t)/(1+t))dt ,where "g" is a continuous odd function. If int_(-pi/2)^( pi/2)(f(x)+(x^(2)cos x)/(1+e^(x)))dx=((pi)/(alpha))^(2)-alpha ,then alpha is equal to

Let f(x)=(e^(x))/(1+x^(2)) and g(x)=f'(x) , then

If x gt0 and g is bounded function then lim_(xtooo)(f(x)e^(nx)+g(x))/(e^(nx)+1)

Let f(x) be the continuous function such that f(x)= (1-e^(x))/(x) for x!=0 then

Let f(x)=(e^(x)x cos x-x log_(e)(1+x)-x)/(x^(2)),x!=0 If f(x) is continuous at x=0, then f(0) is equal to

For the function f(x) = (e^(1/x) -1)/(e^(1//x) + 1) , x=0 , which of the following is correct .