Approximation of ex using maclaurin series in python

When it comes to approximating the value of ex using the Maclaurin series in Python, there are several approaches you can take. In this article, we will explore three different methods to solve this problem.

Method 1: Using the math module

The first method involves utilizing the built-in math.exp() function provided by the math module in Python. This function calculates the exponential value of a given number. To use this method, you need to import the math module at the beginning of your code.

import math

x = 2.5
approximation = math.exp(x)
print(approximation)

This code snippet imports the math module and assigns the value of x as 2.5. It then calculates the approximation of ex using the math.exp() function and stores it in the approximation variable. Finally, it prints the result.

Method 2: Implementing the Maclaurin series formula

The second method involves implementing the Maclaurin series formula manually. The formula for approximating ex using the Maclaurin series is:

ex = 1 + x + (x2/2!) + (x3/3!) + …

To implement this formula in Python, you can use a loop to calculate each term and sum them up.

x = 2.5
approximation = 1
term = 1
factorial = 1

for i in range(1, 10):
    term *= x / i
    factorial *= i
    approximation += term

print(approximation)

This code snippet initializes the variables approximation, term, and factorial to their respective initial values. It then uses a loop to calculate each term of the Maclaurin series and adds it to the approximation. Finally, it prints the result.

Method 3: Using the sympy library

The third method involves using the sympy library, which provides powerful symbolic computation capabilities in Python. With sympy, you can easily define and manipulate mathematical expressions.

import sympy

x = sympy.Symbol('x')
approximation = sympy.exp(x).series(x, 0, 10).removeO()
print(approximation.subs(x, 2.5))

This code snippet imports the sympy module and defines x as a symbolic variable. It then uses the sympy.exp() function to define the exponential expression. The .series() method is used to calculate the Maclaurin series expansion up to the 10th term, and the .removeO() method removes the higher-order terms. Finally, it substitutes the value of x with 2.5 and prints the result.

After exploring these three methods, it is evident that using the math module’s math.exp() function is the simplest and most straightforward approach. It requires minimal code and provides accurate results. Therefore, Method 1 is the recommended option for approximating ex using the Maclaurin series in Python.

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8 Responses

    1. I have to disagree with you there. Method 2 is tried and true, while Method 3 might just be an unnecessary complication. Stick with what works, my friend. #practicalityoverfanciness

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