# How to calculate limits in Matlab and Octave

To calculate a limit of a function f(x) in Matlab and Octave use the function limit()

limit(x,x,xo,['right'/'left'])

The command parameters are

• f is the function f(x)
• x is the limit variable
• x0 is an accumulation point or infinite (inf)
• 'right'/'left' are optional parameters to calculate the right limit or the left limit.

## Examples

Example 1

Define the variable x symbol

syms x

Calculate the limit of the function for x→∞

$$\lim_{x \rightarrow \infty} \frac{1}{x}$$

Type the command

limit(1/x,x,inf)

The output result is the limit for x→∞

ans = (sym) 0

The limit of the function for x→∞ is 0

Example 2

Calculate the limit of the function for x→2

$$\lim_{x \rightarrow 2} \frac{1}{x}$$

Type the command

limit(1/x,x,2)

The output result is the limit for x→2

ans = (sym) 1/2

The limit of the function for x→2 is 1/2

Example 3

Calculate the right limit of the function for x→0+

$$\lim_{x \rightarrow 0^+} \frac{1}{x}$$

Type the command

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

The output result is the limit for x→0+

ans = (sym) ∞

The limit of the function for x→0+ is +∞

Example 4

Calculate the left limit of the function for x→0-

$$\lim_{x \rightarrow 0^-} \frac{1}{x}$$

Type the command

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

The output result is the limit for x→0-

ans = (sym) -∞

The limit of the function for x→0- is -∞

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Calculus in Matlab/Octave