limit

Limit of symbolic expression

Syntax

limit(f,var,a)
limit(f,a)
limit(f)
limit(f,var,a,'left')
limit(f,var,a,'right')

Description

example

limit(f,var,a) returns the Bidirectional Limit of the symbolic expression f when var approaches a.

limit(f,a) uses the default variable found by symvar.

limit(f) returns the limit at 0.

example

limit(f,var,a,'left') returns the Left Side Limit of f as var approaches a.

example

limit(f,var,a,'right') returns the Right Side Limit of f as var approaches a.

Examples

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Calculate the bidirectional limit of this symbolic expression as x approaches 0.

syms x h
f = sin(x)/x;
limit(f,x,0)
ans =
1

Calculate the limit of this expression as h approaches 0.

f = (sin(x+h)-sin(x))/h;
limit(f,h,0)
ans =
cos(x)

Calculate the right and left limits of symbolic expressions.

syms x
f = 1/x;
limit(f,x,0,'right')
ans =
Inf
limit(f,x,0,'left')
ans =
-Inf

Calculate the limit of expressions in a symbolic vector. limit acts element-wise on the vector.

syms x a
V = [(1+a/x)^x exp(-x)];
limit(V,x,Inf)
ans =
[ exp(a), 0]

Input Arguments

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Input, specified as a symbolic expression, function, vector, or matrix.

Independent variable, specified as a symbolic variable. If you do not specify var, then symvar determines the independent variable.

Limit point, specified as a number or a symbolic number, variable, or expression.

More About

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Bidirectional Limit

L=limxaf(x),xa\{0}.

Left Side Limit

L=limxaf(x),xa<0.

Right Side Limit

L=limxa+f(x),xa>0.

See Also

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Introduced before R2006a