Problem 4 4. The purpose of this problem is to make sure you know that the bound on ƒ(n+1) (§) after all the cancellation is NOT necessarily 1 NOR does it have to look the same as the next term in the series. 4.1)Find the first 3 non-zero terms of Taylor series for 1 4.2) If we estimate f(x) = 1 1 - x 1 1 0.8 1 -0.2 using the first 3 non-zero terms, what is the bound on the truncation error. Be careful about evaluating the bound for f(n+1) (§). 1 4.3) How many terms do wee need to calculate 1/(1 – 0.2) such that the uncertainty is less than 10e-5. 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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%matplotlib inline
import numpy as np
from matplotlib import pyplot as plt
import math

Problem 4
4. The purpose of this problem is to make sure you know that the bound on ƒ(n+1) (§) after all the cancellation is NOT necessarily 1 NOR does it have to look the same as the next term
in the series.
4.1)Find the first 3 non-zero terms of Taylor series for
1
4.2) If we estimate
f(x)
=
1
1 - x
1
1
0.8
1 -0.2
using the first 3 non-zero terms, what is the bound on the truncation error. Be careful about evaluating the bound for f(n+1) (§).
1
4.3) How many terms do wee need to calculate 1/(1 – 0.2) such that the uncertainty is less than 10e-5.
1
Python
Python
Python
Transcribed Image Text:Problem 4 4. The purpose of this problem is to make sure you know that the bound on ƒ(n+1) (§) after all the cancellation is NOT necessarily 1 NOR does it have to look the same as the next term in the series. 4.1)Find the first 3 non-zero terms of Taylor series for 1 4.2) If we estimate f(x) = 1 1 - x 1 1 0.8 1 -0.2 using the first 3 non-zero terms, what is the bound on the truncation error. Be careful about evaluating the bound for f(n+1) (§). 1 4.3) How many terms do wee need to calculate 1/(1 – 0.2) such that the uncertainty is less than 10e-5. 1 Python Python Python
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