Holistic Numerical Methods

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

(All Tests)

BISECTION METHOD

(More on Bisection Method)

NONLINEAR EQUATIONS

(More on Nonlinear Equations)

 

Pick the most appropriate answer.

Q1. The bisection method of finding roots of nonlinear equations falls under the category of a (an) ______  method.

open
 bracketing
 graphical

random

Q2. If for a real continuous function f(x), you have f(a)f(b)<0, then in the interval [a,b] for f(x)=0, there is (are)
one root
 an undeterminable number of roots
 no root
 at least one root

Q3. Assuming an initial bracket of [1,5] , the second (at the end of 2 iterations) iterative value of the root of is
 0.0
 1.5
 2.0
 3.0

To find the root of f(x)=0, a scientist uses the bisection method.  At the beginning of an iteration, the lower and upper guesses of the root are xl and xu, respectively.  At the end of this iteration, the absolute relative approximate error in the estimated value of the root would be



 

For an equation like , a root exists at x=0.  The bisection method cannot be adopted to solve this equation in spite of the root existing at  x=0  because the function
is a polynomial
 has repeated roots at x=0
 is always non-negative
 has a slope of zero at x=0

The ideal gas law is given by 

     

where where p is the pressure, v is the specific volume, R is the universal gas constant, and T is the absolute temperature.  This equation is only accurate for a limited range of pressure and temperature.  Vander Waals came up with an equation that was accurate for larger range of pressure and temperature given by

      

 

where a and b are empirical constants dependent on a particular gas.  Given the value of R=0.08, a=3.592, b=0.04267, p=10 and T=300 (assume all units are consistent), one is going to find the specific volume, v, for the above values.  Without finding the solution from the Vander Waals equation, what would be a good initial guess for v?
 0
 1.2
 2.4
 4.8

Complete Solution

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# 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.

  

ANALYTICS