The coefficient of the r term in the Maclaurin polynomial for sin(2x) is (A) 0 (B) 0.0083333 (C) 0.016667 (D) 0.26667 17.
The coefficient of the r term in the Maclaurin polynomial for sin(2x) is (A) 0 (B) 0.0083333 (C) 0.016667 (D) 0.26667 17.
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:17.
The coefficient of the x' term in the Maclaurin polynomial for sin(2x) is
(A) 0
(B) 0.0083333
(C) 0.016667
(D) 0.26667
Given f(3) = 6, f'(3)= 8, f"(3) =11, and that all other higher order derivatives of
f(x) are zero at x = 3, and assuming the function and all its derivatives exist and are
continuous between x= 3 and x= 7, the value of f(7) is
18.
(A) 38.000
(B) 79.500
(C) 126.00
(D) 331.50
Given that y(x) is the solution to
dx
=y +2, y(0) = 3 the value of y(0.2) from a
19.
second order Taylor polynomial written around x =0 is
(A) 4.400
(B) 8.800
(C) 24.46
(D) 29.00
The series (-1)"-
20.
,4" is a Maclaurin series for the following function
(2n)!
(A) cos(x)
(B) cos(2x)
(C) sin(x)
(D) sin(2x)
21.
The function
dt
is called the error function. It is used in the field of probability and cannot be
calculated exactly for finite values of x. However, one can expand the integrand as a
Page 4 of 5
Taylor polynomial and conduct integration. The approximate value of erf (2.0) using
the first three terms of the Taylor series around t = 0 is
(A) -0.75225
(B) 0.99532
(C) 1.5330
(D) 28586
Transcribed Image Text:22.
Using the remainder of Maclaurin polynomial of n* order for f(x) defined as
R.(r)= ,
-glas(c), n20, 0sesx
(n +1)
the least order of the Maclaurin polynomial required to get an absolute true error of at
most 10* in the calculation of sin(0.1) is (do not use the exact value of sin(0.1) or
cos(0.1) to find the answer, but the knowledge that |sin(x)| S1 and | cos(x) |S 1).
(A) 3
(В) 5
(C) 7
(D) 9
23.
The Maclaurin series expansion for cos x is
cos(x) =1-
2!
4!
6!
Starting with the simplest version, cos x = 1, add terms one at a time to estimate
cos(z/3). After each new term is added, compute the true and approximate percent
relative errors. Use your pocket calculator to detemine the true value. Add terms
until the absolute value of the approximate error estimate falls below an error
criterion conforming to two significant figures.
24.
Perform the same computation as in Prob. 23, but use the Maclaurin series expansion
for the sin x to estimate sin(n/3).
sin(x) =x-+
3!
5!
7!
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