Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate

 

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MULTIPLE CHOICE TEST

(All Tests)

TAYLOR SERIES

(More on Taylor Series)

INTRO TO SCIENTIFIC COMPUTING

(More on Scientific Computing)


Pick the most appropriate answer.


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


 

 

Complete solution 

 

 

    


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Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# Creative Commons License0126793, 0341468, 0717624,  0836981, 0836916, 0836805, 1322586.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.  Based on a work at http://mathforcollege.com/nm.  Holistic Numerical Methods licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

 

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