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limit/multi - multidimensional limits

Calling Sequence

limit(f, point)

limit(f, point, dir)

Parameters

f

-

algebraic expression

point

-

set of equations of the form x=a

dir

-

(optional) direction

Description

• 

The limit(f, point) calling sequence attempts to compute the limiting value of f in a multidimensional space at point.

• 

An equation of the form x=x in the limiting point is ignored.

• 

If the limit depends on the direction of approach, undefined is returned.

• 

The optional direction dir is applied to all coordinates in point, and consequently each coordinate is approached from the same direction; from the left or right, bidirectional (real), or complex.

Examples

limitx2y2x2+y2,x=0

1

(1)

limitx2y2x2+y2,x=0,y=0

undefined

(2)

limitx+1y,x=0,y=∞

0

(3)

limitxy,x=0,y=∞

undefined

(4)

limitx3+y3x2+xy+y2,x=0,y=0

0

(5)

limitx3y2x4+y4,x=0,y=0

undefined

(6)

limitx4y2+3x2yx2x2+y2,x=0,y=0

1

(7)

limitsinx2siny2xy,x=0,y=0

limitsinx2siny2xy,x=0,y=0

(8)

limit1yx,x=y

undefined

(9)

limit1yx,x=y,right

∞

(10)

limit1yx,x=y,left

∞

(11)

See Also

limit, limit/dir, limit/return

References

  

Carlos A. Dadavid, Sergio Molina, Juan D. Velez, Limits of quotients of real analytic functions in two variables, arXiv:1011.1591v1, 6 November 2010


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