Taylor-Series-Python-Implementation

Why Taylor Series is important

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• Calculate approximate values of almost every important function on calculators and computers
• Computing transcendental functions such as e^x, sinx, and cosx.
• Taylor series is used to expand the functions. For example you want to know the expansion of sin(x), you can use Taylor series to implement it.

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How single, double and triple differentiations are calculated

For this please look at these functions which I have created in the code

#this is for function f(x)
def fun(y):
    return math.sin(y)
#this is for first derivative of function f(x)
def deri(y):
    return math.cos(y)
#this is for second derivative of function f(x)
def doubleder(y):
    return -math.sin(y)
#this is for third derivative of function f(x)
def triple(y):
    return -math.cos(y)

Limitation of this code

This code is used to find the approximate value till 4 terms. This is only for sin(x) expansion.

How to run this file

Just run the file taylor_series.py using python taylor_series.py and enter the value of variable which is x in the taylor series.