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MULTIPLE CHOICE TEST

(All Tests)

NEWTON-RAPHSON METHOD

(More on Newton-Raphson Method)

NONLINEAR EQUATIONS

(More on Nonlinear Equations)

Pick the most appropriate answer.

Newton-Raphson method of finding roots of nonlinear equations falls under the category of _______ method.
bracketing

open

random

graphical

The Newton-Raphson method formula for finding the square root of a real number R from the equation

is,

 

 

The next iterative value of the root of using Newton-Raphson method, if the initial guess is 3 is
1.500

2.066

2.166

3.000

The root of equation f(x)=0  is found by using Newton-Raphson method.  The initial estimate of the root is x0=3, and f(3)=5.  The angle the tangent to the function f(x) makes at x=3 with the x-axis is 570.  The next estimate of the root, x1 most nearly is
-3.247

-0.2470

3.247

6.247

The root of is found by using Newton-Raphson method.  The successive iterative values of the root are given in the table below

Iteration Number

Value of Root

0

2.0000

1

1.6667

2

1.5911

3

1.5874

4

1.5874

The iteration number at which I would first trust at least two significant digits in the answer is

1

2

3

4

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

 

Multiple choice questions on other topics

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 and 0717624.  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.