Problem 3 Notice that tan(1) = π/4, this means we can calculate π by using 4 × arctan(1) So this means that if we find Taylor series expansion of arctan(x) around x = 0, then we can calculate π to any accuracy we want. 3.1) Find taylor expansion of arctan for 3 non-zero terms. If you forgot, 1 3.2) Guess the rest of the terms 1 d dx 1 arctan(2) 1+x² 3.3) Calculate π using taylor approximation for 200 non-zero terms. (you must write some sort of for loop to do it). 1 Python Python Python

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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given

%matplotlib inline
import numpy as np
from matplotlib import pyplot as plt
import math

Problem 3
Notice that tan(1) = π/4, this means we can calculate π by using 4 × arctan(1)
So this means that if we find Taylor series expansion of arctan(x) around x = 0, then we can calculate π to any accuracy we want.
3.1) Find taylor expansion of arctan for 3 non-zero terms. If you forgot,
1
3.2) Guess the rest of the terms
1
d
dx
1
arctan(2)
1+x²
3.3) Calculate π using taylor approximation for 200 non-zero terms. (you must write some sort of for loop to do it).
1
Python
Python
Python
Transcribed Image Text:Problem 3 Notice that tan(1) = π/4, this means we can calculate π by using 4 × arctan(1) So this means that if we find Taylor series expansion of arctan(x) around x = 0, then we can calculate π to any accuracy we want. 3.1) Find taylor expansion of arctan for 3 non-zero terms. If you forgot, 1 3.2) Guess the rest of the terms 1 d dx 1 arctan(2) 1+x² 3.3) Calculate π using taylor approximation for 200 non-zero terms. (you must write some sort of for loop to do it). 1 Python Python Python
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