If `lim_(xtooo) f(x)` exists and is finite and nonzero and if `lim_(xtooo) {f(x)+(3f(x)-1)/(f^(2)(x))}=3`, then the value of `lim_(xtooo) f(x)" is "`_______.

Answer

`(1)`

Explanation

`underset(xtooo)lim(f(x)+(3f(x)-1)/(f^(2)(x)))=3`
or `(underset(xtooo)limf(x)+(3underset(xtooo)limf(x)-1)/((underset(xtooo)limf(x))^(2)))=3`
or `(y+(3y-1)/(y^(2)))=3`
or `y^(3)-3y^(2)+3y-1=0`
or `(y-1)^(3)=0`
or `y=1`