limit - Compute limit of symbolic expression

Syntax

Description

limit(expr,x,a) computes bidirectional limit of the symbolic expression expr when x approaches a.

limit(expr,a) computes bidirectional limit of the symbolic expression expr when the default variable approaches a.

limit(expr) computes bidirectional limit of the symbolic expression expr when the default variable approaches 0.

limit(expr,x,a,'left') computes the limit of the symbolic expression expr when x approaches a from the left.

limit(expr,x,a,'right') computes the limit of the symbolic expression expr when x approaches a from the right.

Examples

Compute bidirectional limits for the following expressions:

syms x h
limit(sin(x)/x)
limit((sin(x + h) - sin(x))/h, h, 0)

ans =
1
 
ans =
cos(x)

Compute the limits from the left and right for the following expressions:

syms x
limit(1/x, x, 0, 'right')
limit(1/x, x, 0, 'left')

ans =
Inf
 
ans =
-Inf

Compute the limit for the functions presented as elements of a vector:

syms x a
v = [(1 + a/x)^x, exp(-x)];
limit(v, x, inf)

ans =
[ exp(a), 0]

See Also

diff | taylor

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