Let `f(x)=xsin(e^(1/x))` for `x!=0 and` for `x=0` which of the following is true ?

Let F(x)={(x-1)(sin1)/(x-1),x!=1,{0,x=1 then which one of the following is true.

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

Let F(x) be such that F((1-x)/(1+x))=x for all x!=-1 which of the following statements is true

Let y=f(x) ={{:(e^((1)/(x^(2))), if x ne 0),( 0, if x=0):} then which of the following can best represent the graph of y=f(x)?