# Rational functions answers

Recent questions in Rational functions
Rational functions

### 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. $$\displaystyle\lim_{{x} \rightarrow \infty}\frac{{{x}−{3}}}{{\sqrt{{4}{x}^{{2}}+{25}}}}$$

Rational functions

### Determine the domains of the given rational functions. $$\displaystyle\frac{{{x}^{{2}}-{9}}}{{{x}^{{3}}-{x}}}$$

Rational functions

### What formula do we need, in addition to: $$\displaystyle\frac{{d}}{{\left.{d}{x}\right.}}{\left({x}^{{n}}\right)}={n}{x}^{{{n}-{1}}}$$ $$\displaystyle\frac{{d}}{{\left.{d}{x}\right.}}{\left({c}{u}\right)}={c}{d}\frac{{u}}{{\left.{d}{x}\right.}}$$ $$\displaystyle\frac{{d}}{{\left.{d}{x}\right.}}{\left({u}_{{1}}+{u}_{{2}}+\ldots+{u}_{{n}}\right)}={d}\frac{{u}_{{1}}}{{\left.{d}{x}\right.}}+{d}\frac{{u}_{{2}}}{{\left.{d}{x}\right.}}+\ldots+{d}\frac{{u}_{{n}}}{{\left.{d}{x}\right.}}$$ to differentiate rational functions?

Rational functions

### 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). $$\displaystyle{f{{\left({x}\right)}}}=\frac{{{40}{x}^{{5}}+{x}^{{2}}}}{{{16}{x}^{{4}}−{2}{x}}}$$

Rational functions

### In your own words, summarize the guidelines for finding limits at infinity of rational functions.

Rational functions