Graph the rational functions. \(y=x/((x^2)-2)\)

expert advice

Graph the rational functions. \(\displaystyle{y}={\frac{{{\left({x}^{{{3}}}\right)}+{x}-{2}}}{\left({x}-{\left({x}^{{{2}}}\right))}\right.}}\)

Use substitution to convert the integrals to integrals of rational functions. Then use partial fractions to evaluate the integrals. \(\displaystyle\int{\frac{{{1}}}{{{2}+{e}^{{-{x}}}}}}{\left.{d}{x}\right.}\)

Determine \(\displaystyle\lim_{x→∞}{f{{\left({x}\right)}}}\) and \(\displaystyle\lim_{x→−∞}{f{{\left({x}\right)}}}\) for the following rational functions. Then give the horizontal asymptote of f (if any). \(\displaystyle{f{{\left({x}\right)}}}=\frac{{{40}{x}^{{5}}+{x}^{{2}}}}{{{16}{x}^{{4}}−{2}{x}}}\)