limit/multi
multidimensional limits
Calling Sequence
Parameters
Description
Examples
References
Compatibility
limit(f, point)
limit(f, point, dir)
f
-
algebraic expression
point
set or list of equations of the form x=a
dir
(optional) direction
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, either a range or undefined is returned (see limit,return).
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.
limitx2−y2x2+y2,x=0
−1
limitx2−y2x2+y2,x=0,y=0
−1..1
limitx+1y,x=0,y=∞
0
limitxy,x=0,y=∞
undefined
limitx3+y3x2+xy+y2,x=0,y=0
limitx3y2x4+y4,x=0,y=0
−634216..634216
limitx4−y2+3x2y−x2x2+y2,x=0,y=0
limitsinx2−siny2x−y,x=0,y=0
limit1y−x,x=y
limit1y−x,x=y,right
−∞
limit1y−x,x=y,left
∞
C. Cadavid, S. Molina, J.D. Velez, Limits of quotients of bivariate real analytic functions, Journal of Symbolic Computation, Volume 50, March 2013, 197-207, doi:10.1016/j.jsc.2012.07.004
Gary R. Lawlor, l'Hôpital's Rule for Multivariable Functions, The American Mathematical Monthly, 127:8 (2020), 717-725, doi:10.1080/00029890.2020.1793635
The limit/multi command was updated in Maple 2021.
See Also
limit
limit/dir
limit/return
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