Holistic Numerical Methods

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MULTIPLE CHOICE TEST

(All Tests)

LAGRANGIAN INTERPOLATION

(More on Lagrangian Interpolation)

INTERPOLATION

(More on Interpolation)


Pick the most appropriate answer.


Q1. Given n+1 data pairs, a unique polynomial of degree ____ passes through the n+1 data points.
n+1
n
n or less
greater than n


Q2. Given the two points , the linear Lagrange polynomial  that passes through these two points is given by

 

 

 

 


Q3. The Lagrange polynomial that passes through three data points is given by

x

15

18

22

y

24

37

25

  

 The value of at x = 16 is

0.071430
0.50000
0.57143
4.3333


Q4. The following data of the velocity of a body is given as a function of time.

Time (s)

10

15

18

22

24

Velocity (m/s)

22

24

37

25

123

A quadratic Lagrange interpolant is found using three data points, t=15, 18 and 22.  From this information, at what of the times given in seconds is the velocity of the body 26 m/s during the time interval of t=15 to 22 seconds.

20.173
21.858
21.667
22.020


Q5. The path that a robot is following on a x-y plane is found by interpolating four data points as

x

2

45

5.5

7

y

7.5

7.5

6

5

 

 

The length of the path from x = 2 to x = 7 is


 


Q6. The following data of the velocity of a body is given as a function of time.

Time (s)

0

15

18

22

24

Velocity (m/s)

22

24

37

25

123

 If you were going to use quadratic interpolation to find the value of the velocity at t=14.9 seconds, what three data points of time would you choose for interpolation?  Justify your answer.

0, 15, 18
15, 18, 22
0, 15, 22
0, 18, 24


 

Complete solution

 

 

Multiple choice questions on other topics


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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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