Suppose you want to approximate sin x with the sixth-order Maclaurin series: х3 х5 х7 + 5! sin x = x + 7! -- | - - 3! Which of the following calculations would produce the most truncation error? a. sin п 10 b. sin c. sin n d. sin 27 e. They would all have equal error for a sixth-order series.
Suppose you want to approximate sin x with the sixth-order Maclaurin series: х3 х5 х7 + 5! sin x = x + 7! -- | - - 3! Which of the following calculations would produce the most truncation error? a. sin п 10 b. sin c. sin n d. sin 27 e. They would all have equal error for a sixth-order series.
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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![2. Suppose you want to approximate sin x with the sixth-order Maclaurin series:
\[
\sin x \approx x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots
\]
Which of the following calculations would produce the most truncation error?
a. \( \sin \frac{\pi}{10} \)
b. \( \sin \frac{\pi}{2} \)
c. \( \sin \pi \)
d. \( \sin 2\pi \)
e. They would all have equal error for a sixth-order series.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79826512-1148-4736-b4a7-6e7f4ec13f28%2F4ea35102-cd2f-4c15-ad5c-df9866a5c782%2F22jjtnk_processed.png&w=3840&q=75)
Transcribed Image Text:2. Suppose you want to approximate sin x with the sixth-order Maclaurin series:
\[
\sin x \approx x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots
\]
Which of the following calculations would produce the most truncation error?
a. \( \sin \frac{\pi}{10} \)
b. \( \sin \frac{\pi}{2} \)
c. \( \sin \pi \)
d. \( \sin 2\pi \)
e. They would all have equal error for a sixth-order series.
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