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

$$\lim_{x\to\pm\infty}k=k\hspace{2cm}\lim_{x\to\pm\infty}\frac{1}{x}=0$$ These results can be extended to help calculate other limits of function as $x$ approaches $\infty$, because according to Theorem 12, all of the limit laws listed in Theorem 1 used for limits as $x\to c$ can also be applied to these limits as $x\to\pm\infty$.
$$\lim_{x\to\pm\infty}k=k\hspace{2cm}\lim_{x\to\pm\infty}\frac{1}{x}=0$$ These results can be extended to help calculate other limits of function as $x$ approaches $\infty$, because according to Theorem 12, all of the limit laws listed in Theorem 1 used for limits as $x\to c$ can also be applied to these limits as $x\to\pm\infty$. For example, $\lim_{x\to\infty}\frac{109}{x}=\lim_{x\to\infty}109\times\lim_{x\to\infty}\frac{1}{x}=109\times0=0$ $\lim_{x\to\infty}\frac{1}{2x}=\lim_{x\to\infty}\frac{1}{2}\times\lim_{x\to\infty}\frac{1}{x}=\frac{1}{2}\times0=0$ $\lim_{x\to-\infty}\frac{\pi\sqrt3}{x^2}=\lim_{x\to-\infty}\pi\sqrt3\times\lim_{x\to-\infty}\frac{1}{x}\times\lim_{x\to-\infty}\frac{1}{x}=\pi\sqrt3\times0\times0=0$