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.
the graphic interface of Octave

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. $$ \lim_{x \rightarrow + \infty} \frac{x+1}{x-1} = 1 $$ the graph of the function as x tends to infinity

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. $$ \lim_{x \rightarrow - \infty} \frac{x+1}{x-1} = 1 $$ the graph of the function that tends to minus infinity

To evaluate a limit of x approaching x₀, where a is x₀ 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. $$ \lim_{x \rightarrow 2} \frac{x+1}{x-1} = 3 $$ the limit of the function for x tending to 2

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. $$ \lim_{x \rightarrow 1^+} \frac{x+1}{x-1} = + \infty $$ the hand right limit of the function as x approaches one

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. $$ \lim_{x \rightarrow 1^-} \frac{x+1}{x-1} = - \infty $$ the left hand limit of the function as x approaches one

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