## University Calculus: Early Transcendentals (3rd Edition)

$\infty$
L'Hospital's rule states that $\lim\limits_{x \to \infty} f(x)=\lim\limits_{x \to \infty} \dfrac{A'(x)}{B'(x)}$ Here, $\lim\limits_{x \to \infty} f(x)=\lim\limits_{x \to \infty} (\sqrt {x^3+1}-\sqrt x)$ or, $\lim\limits_{x \to \infty} (\sqrt {x^3+1}-\sqrt x)=\lim\limits_{x \to \infty} x (\dfrac{\sqrt {x^3+1}}{x}-\dfrac{\sqrt x}{x})$ or, $\lim\limits_{x \to \infty} (\sqrt {1+1/x^2}-\sqrt{\dfrac{1}{x}})=\lim\limits_{x \to \infty} (x)(1)=\infty$