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 MULTIPLE CHOICE TEST TAYLOR SERIES INTRO TO SCIENTIFIC COMPUTING

Q1. The coefficient of the x5 term in the Maclaurin polynomial for sin(2x) is

0

0.0083333

0.016667

0.26667

Q2. Given f(3)=6, f'(3)=8, and 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

38.000

79.500

126.00
331.50

Q3. Given that y(x) is the solution to dy/dx=y3+2, y(0)=3, the value of y(0.2) from a second order Taylor polynomial is

4.400
8.800

24.46

29.00

Q4. The series

is a Maclaurin series for the following function

cos(x)

cos(2x)

sin(x)

sin(2x)

Q5. The function

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 Taylor polynomial and conduct integration.  The approximate value of erf(2.0) using first three terms of the Taylor series around t=0 is

-0.75225
0.99532

1.5330

2.8586

Q6. Using the remainder of Maclaurin polynomial of nth order for f(x) defined as

the least order of the Maclaurin polynomial required to get an absolute true error of at most 10-6 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)|1 and |cos(x)|1).

3
5
7

9

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