limit - Compute limit of symbolic expression

Syntax

limit(expr, x, a) limit(expr, a) limit(expr) limit(expr, x, a, 'left') limit(expr, x, a, 'right')

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.

Compute bidirectional limits for the following expressions:

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

The results are

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')

The results are

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)

The result is

ans =
[ exp(a), 0]