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 -∞
