Answer
$2$
Work Step by Step
$x$ is "approaching $+\infty$" means that $x$ is getting larger and larger without bound.
See table below.
As we make $x$ greater and greater, the function value approaches the value $2$.
So, we write
$\displaystyle \lim_{x\rightarrow\infty}\frac{6x^{2}+5x+100}{3x^{2}-9}=2$
