Answer
$\dfrac{5}{7}$
Work Step by Step
Consider: $\lim\limits_{x \to \infty}f(x)=\lim\limits_{x \to \infty}\dfrac{5x^2-3x}{7x^2+1}$
Now, $f(\infty)=\dfrac{\infty}{\infty}$
The limit shows an indeterminate form. Thus, apply L-Hospital's rule: $\lim\limits_{a \to b}f(x)=\lim\limits_{a \to b}\dfrac{g'(x)}{h'(x)}$
This implies:
$\lim\limits_{x \to \infty}\dfrac{10x-3}{14x}=\dfrac{\infty}{\infty}$
Now, again apply L-Hospital's rule:
$\lim\limits_{x \to \infty}\dfrac{10}{14}=\dfrac{5}{7}$