How to calculate a limit of a function in python

To find the limit of a mathematical function in python, we can use limit() function of the sympy library.

limit(y,x,x0,s)

• The first argument (y) is the functionf (x) whose limit is to be calculated
• The second parameter (x) is the reference variable ( argument )
• The third parameter (x0) is the accumulation point
  
  • oo = + infinity
  • -oo = - infinity
  • 0 = zero
  • n = number
• The fourth parameter (s) is used to calculate the lateral limits of a point
  • '+' =right limit
  • '-' = left limit

The function limit() calculates the limit of the function f (x) as x approaches x₀.

$$ \lim_{x \rightarrow x_0 } f(x) = l $$

What's a limit of a function? The limit of a function f(x) at X₀ point in its domain, if it exists, is the value that the function f(x) approaches as its argument approaches X₀. The notation of a limit is as follows: $$ \lim_{x \rightarrow x_0 } f(x) = l $$ We can read "the limit of f(x) as x approaches x₀ is L".

The limit() function must be imported from the sympy library using the command from sympy import limit.

Examples

Example 1

This script calculates the limit of the function 1/x as x approaches zero.

from sympy import limit, Symbol
x = Symbol('x')
y=1/x
limit(y, x, 0)

The function returns to output

oo

The limit of the function 1 / x as x approaches zero is more infinite (oo).

$$ \lim_{x \rightarrow 0 } \frac{1}{x} = \infty $$

Example 2

This script calculates the limit of the 1/x function as x approaches + infinite.

from sympy import limit, oo, Symbol
x = Symbol('x')
y=1/x
limit(y, x, oo)

The oo symbol (+ infinity) must be imported from sympy.

The output of the function is

0

The limit of the function 1 / x for x tending to +∞ is zero.

$$ \lim_{x \rightarrow \infty } \frac{1}{x} = 0 $$

Example 3

This script calculates the limit of the function x² as x approaches - infinite.

from sympy import limit, oo, Symbol
x = Symbol('x')
y=x**2
limit(y, x, -oo)

The output of the function is

oo

The limit of the function is + infinite.

$$ \lim_{x \rightarrow - \infty } x^2 = \infty $$

Example 4

This script calculates the limit of the x² as x approaches 4.

from sympy import limit, oo, Symbol
x = Symbol('x')
y=x**2
limit(y, x, 4)

The output of the function is

16

The limit of the function for x tending to 4 is 16.

$$ \lim_{x \rightarrow 4 } x^2 = 16 $$

Example 5 (lateral limit)

This script calculates the lateral boundary of the 1 / x function with x tending towards zero from the left.

from sympy import limit, Symbol
x = Symbol('x')
y=1/x
limit(y, x, 0, '-')

The function returns in output

-oo

The limit of the function 1 / x as x tending to zero from the left is minus infinite (-oo).

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