# How to find limit of the function in Octave

How to calculate the **limit of a function in Octave** with some practical examples.

**What do you need?** You must have already installed the GNU Octave open source software on your PC and the Symbolic module.

Define the independent variable x symbol of the function using **syms** on the Octave command line.

syms x

Now calculate limit as x approaches infinity x→∞ of the function f(x)=(x+1)/(x-1)

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

Type the **limit()** command

Write the function name f (x) in the first parameter and the variable name x in the second parameter. Then hit enter.

limit((x+1)/(x-1),x)

Octave calculates the limit of the function as x→∞

ans = (sym) 1

In this case the limit of the function is 1

**Verify**. The limit of the function f(x)=(x+1)/(x-1) as x→∞ is 1. $$ \lim_{x \rightarrow + \infty} \frac{x+1}{x-1} = 1 $$

If you want to calculate the limit as x approaches minus infinity x→-∞, type the same command adding **-inf** in the third parameter

limit((x+1)/(x-1),x,-inf)

The output result is 1

ans = (sym) 1

**Verify**. The limit of the function f(x)=(x+1)/(x-1) as x→-∞ is 1. $$ \lim_{x \rightarrow - \infty} \frac{x+1}{x-1} = 1 $$

To evaluate a **limit of x approaching x**_{0}, where a is x_{0} finite number, type the same command and indicate x0 in the third parameter.

For example, calculate the limit of the function as x tends two (x → 2)

limit((x+1)/(x-1),x,2)

The output result is 3

ans = (sym) 3

**Verify**. The limit of the function f(x)=(x+1)/(x-1) as x→2 is 3. $$ \lim_{x \rightarrow 2} \frac{x+1}{x-1} = 3 $$

If you just want to calculate the **hand right limit**, use the same command and type '**right**' in the fourth parameter.

limit((x+1)/(x-1),x,1,'right')

The output result is infinite ( ∞ )

ans = (sym) ∞

**Verify**. The limit of the function f(x)=(x+1)/(x-1) as x→1^{+} is infinity. $$ \lim_{x \rightarrow 1^+} \frac{x+1}{x-1} = + \infty $$

To calculate the **hand left limit**, use the same command and type '**left**' in the fourth parameter.

limit((x+1)/(x-1),x,1,'left')

The output result is minus infinite ( -∞ )

ans = (sym) -∞

**Verifiy**. The limit of the function f(x)=(x+1)/(x-1) as x→1^{-} is minus infinity. $$ \lim_{x \rightarrow 1^-} \frac{x+1}{x-1} = - \infty $$

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