Asymptotes - Maple Help

Student[Calculus1]

 Asymptotes
 find the asymptotes of an expression

 Calling Sequence Asymptotes(f(x), x, y, opts) Asymptotes(f(x), x = a..b, y, opts) Asymptotes(f(x), a..b, y, opts)

Parameters

 f(x) - algebraic expression in variable 'x' x - name; specify the independent variable y - (optional) name; specify the dependent variable opts - (optional) equation(s) of the form numeric=true or false; specify computation options a, b - algebraic expressions; specify restricted interval for vertical asymptotes

Description

 • The Asymptotes(f(x), x) calling sequence returns all the vertical, horizontal, and diagonal asymptotes of the expression f(x) as a list of equations of the form $x=\mathrm{value}$, $y=\mathrm{value}$, and $y=\mathrm{value}x$, respectively.
 • The Asymptotes(f(x), x = a..b) calling sequence returns all the vertical asymptotes in the interval [a, b], and horizontal and diagonal asymptotes of the expression f(x) as a list of equations of the form $x=\mathrm{value}$, $y=\mathrm{value}$, and $y=\mathrm{value}x+\mathrm{value}$, respectively.
 • The default name of the dependent variable is y unless y is specified as the independent variable.
 • If the independent variable can be uniquely determined from the expression, the parameter x need not be included in the calling sequence.
 • If the expression has an infinite number of vertical asymptotes, a warning message and sample vertical asymptotes are returned.
 • The opts argument can contain the following equation that sets computation options.
 numeric = true or false
 Whether to use numeric methods (using floating-point computations) to find the asymptotes of the expression. If this option is set to true, the points a and b must be finite and are set to $-10$ and $10$ if they are not provided. By default, the value is false.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Calculus1}\right]\right):$
 > $\mathrm{Asymptotes}\left(\frac{1}{x-3}+2x,x\right)$
 $\left[{y}{=}{2}{}{x}{,}{x}{=}{3}\right]$ (1)
 > $\mathrm{Asymptotes}\left(\frac{1}{x-3}+2x,x=0..2\right)$
 $\left[{y}{=}{2}{}{x}\right]$ (2)
 > $\mathrm{Asymptotes}\left(\mathrm{tan}\left(x\right),0..10\right)$
 $\left[{x}{=}\frac{{\mathrm{\pi }}}{{2}}{,}{x}{=}\frac{{3}{}{\mathrm{\pi }}}{{2}}{,}{x}{=}\frac{{5}{}{\mathrm{\pi }}}{{2}}\right]$ (3)
 > $\mathrm{Asymptotes}\left(\mathrm{tan}\left(x\right),0..10,\mathrm{numeric}\right)$
 $\left[{x}{=}{1.570796327}{,}{x}{=}{4.712388981}{,}{x}{=}{7.853981635}\right]$ (4)
 > $\mathrm{Asymptotes}\left(\frac{{x}^{3}-2{x}^{2}+x}{{x}^{3}-3{x}^{2}-x+3},x\right)$
 $\left[{y}{=}{1}{,}{x}{=}{-1}{,}{x}{=}{3}\right]$ (5)