`limit`

Limit of a symbolic expression.

Syntax

L = limit(f, x, a)

Limit of f as x approaches a.

L = limit(f, x, a, 'left')

One-sided limit from below.

L = limit(f, x, a, 'right')

One-sided limit from above.

Description

Without a direction, limit returns the two-sided limit, which exists only if both sides agree. For 1/x at 0 the sides disagree, so asking for 'left' and 'right' separately gives -Inf and Inf. Indeterminate forms such as (sin(x)-x)/x^3 at 0 are resolved by series expansion, giving -1/6.

Input arguments

f: Symbolic expression.
x: Symbolic variable.
a: Point, number or Inf.

Output arguments

L: Symbolic limit, possibly Inf, -Inf or NaN.

Example

Limits

syms x
limit((sin(x) - x)/x^3, x, 0)
limit(1/x, x, 0, 'left')
limit(1/x, x, 0, 'right')
limit((1 + 1/x)^x, x, Inf)

Output

ans = -1/6
ans = -Inf
ans = Inf
ans = 1

limit