Answer
$1$
Work Step by Step
Consider $f(x)=\lim\limits_{x \to \infty}(1+\dfrac{2}{x}+\dfrac{7}{x^2})$
or, $\lim\limits_{x \to \infty}(1+\dfrac{2}{x}+\dfrac{7}{x^2})=\lim\limits_{x \to \infty}(1)+\lim\limits_{x \to \infty}(\dfrac{2}{x})+\lim\limits_{x \to \infty}(\dfrac{7}{x^2})$
or, $=1+0+0$
or, $=1$
