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Problem 2 - 40 points The value of sin(x) can be approximated using a Maclaurin series x³ x5 sin(x) = x- + - 3! 5! which can be expressed more compactly as x² 7! +

Problem 2 - 40 points The value of sin(x) can be approximated using a Maclaurin series x³ x5 sin(x) = x- + - 3! 5! which can be expressed more compactly as x² 7! +

Database System Concepts
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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Problem 2 - 40 points The value of sin(x) can be approximated using a Maclaurin series x³ x5 x7 3! 5! 7! sin(x) = x - which can be expressed more compactly as + ∞ x(k-1)*2+1 Σ(−1)k~¹ (k − 1) + 2 + 1)! − * (recall that the symbol ! stands for factorial, i.e., 3!=3×2×1). a) Write a for loop to determine sin(2) using 5 terms (k=5). b) Use a midpoint break loop to determine how many terms must be included in the summation, in order to find the correct value of sin(2) within an error of 0.001. Limit the number of iterations to a maximum of 10. c) Create a function called my_sin to approximate the value of sin(x) for k=10. d) Draw sin(x) using my_sin for x from 0 to 2pi with the intervals of 0.1pi for k=1,3,5 and 7 in one plot.
Transcribed Image Text:Problem 2 - 40 points The value of sin(x) can be approximated using a Maclaurin series x³ x5 x7 3! 5! 7! sin(x) = x - which can be expressed more compactly as + ∞ x(k-1)*2+1 Σ(−1)k~¹ (k − 1) + 2 + 1)! − * (recall that the symbol ! stands for factorial, i.e., 3!=3×2×1). a) Write a for loop to determine sin(2) using 5 terms (k=5). b) Use a midpoint break loop to determine how many terms must be included in the summation, in order to find the correct value of sin(2) within an error of 0.001. Limit the number of iterations to a maximum of 10. c) Create a function called my_sin to approximate the value of sin(x) for k=10. d) Draw sin(x) using my_sin for x from 0 to 2pi with the intervals of 0.1pi for k=1,3,5 and 7 in one plot.
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