If $\underset{x→∞}{\lim}f (x)$ exists and is finite and $\underset{x→∞}{\lim}\begin{pmatrix}f(x)+\frac{3f(x)-1}{(f(x))^2}\end{pmatrix}=3$, then the value of $\underset{x→∞}{\lim}f (x)$ is
Answer & explanation
Correct answer: option 1
Let $\underset{x→∞}{\lim}f (x)=l$
$∴ l+\frac{3l-1}{l^2}=3⇒l^3-3l^2+3l-1=0⇒(l-1)^3=0⇒l=1$