Question

# The process by which we determine limits of rational functions applies equally well to ratios containing noninteger or negative powers of x: Divide nu

Rational functions
$$\displaystyle\lim_{{{x}\rightarrow-\infty}}{\frac{{\sqrt{{{x}^{{{2}}}+{1}}}}}{{{x}+{1}}}}$$
$$\displaystyle\lim_{{{x}\to-\infty}}{d}{\frac{{\sqrt{{{d}{\frac{{{x}^{{2}}+{1}}}{{{x}^{{2}}}}}}}}}{{{d}{\frac{{{x}+{1}}}{{{\left|{x}\right|}}}}}}}={d}{\frac{{{1}}}{{-{1}+{0}}}}=-{1}$$