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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=value, y=value, and y=valuex, 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=value, y=value, and y=valuex+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

withStudent[Calculus1]:

Asymptotes1x3+2x,x

y=2x,x=3

(1)

Asymptotes1x3+2x,x=0..2

y=2x

(2)

Asymptotestanx,0..10

x=12π,x=32π,x=52π

(3)

Asymptotestanx,0..10,numeric

x=1.57079632679714,x=4.71238898039149,x=7.85398163397504

(4)

Asymptotesx32x2+xx33x2x+3,x

y=1,x=1,x=3

(5)

See Also

Student, Student[Calculus1], Student[Calculus1][CriticalPoints], Student[Calculus1][CurveAnalysisTutor], Student[Calculus1][ExtremePoints], Student[Calculus1][FunctionChart], Student[Calculus1][InflectionPoints], Student[Calculus1][Roots]


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