1. The Maclaurin series expansion for sin x is sinx=x x³ x5 x7 3! 5! 7! Use the Maclaurin series expansion for the sin x to estimate sin(7/3). After each new term is added, compute the true and approximate percent relative errors. Add terms until the absolute value of the approximate error estimate falls below an error criterion conforming to two significant figures. Note: Use the radian mode on your calculator.
1. The Maclaurin series expansion for sin x is sinx=x x³ x5 x7 3! 5! 7! Use the Maclaurin series expansion for the sin x to estimate sin(7/3). After each new term is added, compute the true and approximate percent relative errors. Add terms until the absolute value of the approximate error estimate falls below an error criterion conforming to two significant figures. Note: Use the radian mode on your calculator.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. The Maclaurin series expansion for sin x is
sinx=x
Use the Maclaurin series expansion for the sin x to estimate sin(7/3). After each new term is added,
compute the true and approximate percent relative errors. Add terms until the absolute value of the
approximate error estimate falls below an error criterion conforming to two significant figures.
Note: Use the radian mode on your calculator.
x³ x5 x7
3! 5! 7!
2. Determine the first root of the function
f(x) = x³ - 4x - 9
with applying Bisection method, use initial guesses of x₂ = 2 and x = 3 with a stopping criterion of
1%.
3. Use the Newton-Raphson method to determine a root of
f(x) = (x - 2)² - In x
Starting with an initial guess as xo-1, perform the computation until E is less than = 0.001%.
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Step 1: Introduction
VIEWStep 2: Specify the error criterion corresponding to 2 significant digits
VIEWStep 3: Approximate sin(π/3) by taking first term
VIEWStep 4: Approximate sin(π/3) by taking first two terms
VIEWStep 5: Approximate sin(π/3) by taking first three terms
VIEWStep 6: Approximate sin(π/3) by taking first four terms
VIEWStep 7: Approximate sin(π/3) by taking first five terms
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