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MULTIPLE CHOICE TEST

(All Tests)

Numerical Differentiation of DISCRETE Functions

(More on Discrete Differentiation)

DIFFERENTIATION

(More on Differentiation)

 

Pick the most appropriate answer.


Q1. The definition of the first derivative of a function f(x) is

 


Q2.  Using forward divided difference with a step size of 0.2, the derivative of the function at x=2 is given as

x

1.8

2.0

2.2

2.4

2.6

f(x)

6.0496

7.3890

9.0250

11.023

13.464

6.697
7.389

7.438
8.179



Q3. A student finds the numerical value of  f ' (x)=20.219 at x=3 using a step size of 0.2. Which of the following methods did the student use to conduct the differentiation if is given in the table below?

x

2.6

2.8

3.0

3.2

3.4

3.6

f(x)

 

Backward Divided Difference

Calculus, that is, exact
Central Divided Difference

Forward Divided Difference



 

Q4. The upward velocity of a body is given as a function of time in the table below.

 

t

 s

10

15

20

22

v

22

36

57

10

 

To find the acceleration at t=17s, a scientist finds a second order polynomial approximation for velocity, and then differentiates it to find the acceleration. The estimate of the acceleration at t=17s in m/s2 most nearly is

4.060

4.200

8.157
8.498



Q5. The velocity of the rocket is given as a function of time in the table below.

 

t (s)

0

0.5

1.2

1.5

1.8

v (m/s)

0

213

223

275

300

 

Allowed to use forward difference, backward difference or central difference approximation of the first derivative, your best estimate for the acceleration (a=dv/dt) of the rocket in m/s2 at t=1.5 seconds is

83.33
128.33

173.33

183.33



 

Q6. In a circuit with an inductor of inductance L, a resistor with resistance R, and a variable voltage source E(t),

       

The current, i, is measured at several values of time as

 

Time, t (s)

1.00

1.01

1.03

1.1

Current, i (amperes)

3.10

3.12

3.18

3.24

 

If L= 0.98 Henries and R=0.142 ohms, your choice for most accurate answer for E(1.00) would be

 

0.98*(3.24-3.10)/0.1+(0.142)(3.10)

0.142*3.10

0.98*(3.12-3.10)/0.01+(0.142)(3.10)

0.98*(3.12-3.10)/0.01


 

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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