Directional limits - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Calculus : Limits : limit/dir

limit/dir - Directional limits

Calling Sequence

limit(f, x=a, left)

limxaf

limit(f, x=a, right)

limxa+f

limit(f, x=a, dir)

Parameters

f

-

algebraic expression

x=a

-

equation, where x is a name and a is the limit point

dir

-

(optional) direction, can be left, right, real , or complex

Description

• 

If dir is left or right, the limit is a directional limit, taken from the left or right, respectively. If dir is real, the limit is the bidirectional real limit. If dir is complex, the limit is omni-directional, from all complex directions to the point.

• 

If dir is not specified, the limit is the real bidirectional limit, except in the case where the limit point is infinity or -infinity, in which case the limit is from the left to infinity or from the right to -infinity respectively.

• 

If dir is complex, the limit point infinity denotes complex infinity, that is, all infinities in the complex plane. If dir is real, the limit point infinity denotes both positive and negative infinity, and the limit is done bidirectionally. Otherwise, the limit point infinity denotes positive infinity, and -infinity denotes negative infinity.

• 

You can enter the command limit using either the 1-D or 2-D calling sequence.

Examples

limx→∞ⅇx

∞

(1)

limx→∞ⅇx

0

(2)

limx→0+1x

∞

(3)

limx→01x

∞

(4)

limx→01x

undefined

(5)

limx→∞x

∞

(6)

Examples using real or complex options

  

To use the real and complex arguments, the limit command must be written in 1-D Math notation.

limit(1/x, x=0, real);

undefined

(7)

limit(1/x, x=0, complex);

∞∞I

(8)

limit(1/x, x=infinity, real);

0

(9)

limit(-x, x=infinity, complex);

∞+∞I

(10)

limit(exp(x), x=infinity,real);

undefined

(11)

See Also

limit, limit/multi, limit/return


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam