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

Question

asked 2021-06-13

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.

\(\displaystyle\lim_{{{x}\rightarrow-\infty}}{\frac{{\sqrt{{{3}}}{\left\lbrace{x}\right\rbrace}-{5}{x}+{3}}}{{{2}{x}+{x}^{{{\frac{{{2}}}{{{3}}}}}}-{4}}}}\)

\(\displaystyle\lim_{{{x}\rightarrow-\infty}}{\frac{{\sqrt{{{3}}}{\left\lbrace{x}\right\rbrace}-{5}{x}+{3}}}{{{2}{x}+{x}^{{{\frac{{{2}}}{{{3}}}}}}-{4}}}}\)

asked 2021-06-26

asked 2021-05-14

asked 2021-06-09

Choose the correct term to complete each sentence. To find the limits of rational functions at infinity, divide the numerator and denominator by the _____ power of x that occurs in the function.