Let $f\mathbb{ }:\mathbb{R}\to \left(0, \infty \right)$ and $g\mathbb{ }:\mathbb{R}\to \mathbb{R}$ be twice differentiable functions such that $f^{″}$ and $g^{″}$ are continuous functions on $\mathbb{R}$ . Suppose $f^{\prime }\left(2\right)=g\left(2\right)=0, f^{″}\left(2\right)\ne 0$ and $g^{\text{'}}\left(2\right)\ne 0$, $\underset{x\to 2}{\lim }\frac{f\left(x\right) g\left(x\right)}{f^{\text{'}} \left(x\right) g^{\text{'}}\left(x\right)}=1$, then