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
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asked 2021-05-22
The process by which we determine limits of rational functions applies equally well to ratios containing noninteger or negative powers of x: Divide numerator and denominator by the highest power of x in the denominator and proceed from there. Find the limits.
\(\displaystyle\lim_{{{x}\rightarrow-\infty}}{\frac{{\sqrt{{{x}^{{{2}}}+{1}}}}}{{{x}+{1}}}}\)

Answers (1)

2021-05-23

\(\displaystyle\lim_{{{x}\to-\infty}}{d}{\frac{{\sqrt{{{d}{\frac{{{x}^{{2}}+{1}}}{{{x}^{{2}}}}}}}}}{{{d}{\frac{{{x}+{1}}}{{{\left|{x}\right|}}}}}}}={d}{\frac{{{1}}}{{-{1}+{0}}}}=-{1}\)

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