Transforming Numerical Methods Education for the STEM Undergraduate MOOC | MOBILE | VIDEOS | BLOG | YOUTUBE | TWITTER | COMMENTS | ANALYTICS | ABOUT | CONTACT | COURSE WEBSITES | BOOKS | MATH FOR COLLEGE
 MULTIPLE CHOICE TEST Numerical Differentiation of DISCRETE Functions DIFFERENTIATION

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 2.2 2.4 2.6 f(x) 6.0496 7.389 9.025 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 1.01 1.03 1.1 Current, i (amperes) 3.1 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

Multiple choice questions on other topics

 AUDIENCE |  AWARDS  |  PEOPLE  |  TRACKS  |  DISSEMINATION  |  PUBLICATIONS 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# 0126793, 0341468, 0717624,  0836981, , 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. ANALYTICS