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limit/return

values returned by limit

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

limit(f, point, dir)

Parameters

f

-

algebraic expression

point

-

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

dir

-

(optional) direction

Description

• 

The meaning of a returned infinity depends on dir. If dir is complex, then infinity denotes complex infinity.  Otherwise, the result infinity denotes real positive infinity, and -infinity denotes real negative infinity.

• 

If limit returns a numeric range it means that the value of the limiting expression is known to lie in that range for arguments restricted to some neighborhood of the limit point.  It does not necessarily imply that the limiting expression is known to achieve every value infinitely often in this range.

• 

If the limit is known to be undefined, or each side of a two-sided limit has a different value, or for a multi-dimensional limit the limiting value depends on the direction from which the limit is approached, then undefined is returned.

• 

If limit is unable to evaluate the limit, then it returns unevaluated. Unless the limit is unevaluated, the limit returned is independent of the variable given in point.

• 

See limit and limit/dir for more information.

Examples

limx→∞ⅇx

∞

(1)

limx→0, complex1x

∞∞I

(2)

limx→0sin1x

1..1

(3)

limx→∞, realⅇx

undefined

(4)

limx→∞tanx

undefined

(5)

limx→∞ax

signuma∞

(6)

See Also

limit

limit/dir

limit/multi

 


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