MATH FOR COLLEGE
Problem Set#1
Multiple Choice Test
Chapter 03.06 False-Positiion Method
COMPLETE SOLUTION SET
1. The false-position method for finding roots of nonlinear equations belongs to a class of a (an) ____________ method.
(A) open
(B) bracketing
(C) random
(D) graphical
Solution
The correct answer is (B).
The false-position method brackets the root with the two initial guesses.
2. The newly predicted root for false-position and secant method can be respectively given as
[pic]
and
[pic] ,
While the appearance of the above 2 equations look essentially identical, and both methods require two initial guesses, the major difference between the above two formulas is
A) false-position method is not guaranteed to converge
B) secant method is guaranteed to converge
C) secant method requires the 2 initial guesses [pic] to satisfy [pic]
D) false-position method requires the 2 initial guesses [pic] to satisfy [pic]
Solution
The correct answer is (D).
In order for the two initial guesses to bracket the root, [pic] must be true. In other words, the function must change signs between the two guesses for there to be a root present.
3. Given are the following nonlinear equation
[pic]
two initial guesses, [pic] and [pic], and a pre-specified relative error tolerance of 0.1%. Using the false-position method, which of the following tables is correct = predicted root)?
A)
|Iteration |[pic] |[pic] |[pic] |
|1 |1 |4 |? |
|2 |? |? |2.939 |
B)
|Iteration |[pic] |[pic] |[pic] |
|1 |1 |4 |? |
|2 |? |? |2.500 |
C)
|Iteration |[pic] |[pic] |[pic] |
|1 |1 |4 |? |
|2 |? |? |1.500 |
D)
|Iteration |[pic] |[pic] |[pic] |
|1 |1 |4 |? |
|2 |? |? |2.784 |
Solution
The correct answer is (A).
First check given function is of the form [pic], then proceed as follows:
Iteration 1:
Initial guesses are [pic] and [pic]. Check that they satisfy the requirement [pic].
[pic], which is 0, the root must lie between [pic] and [pic]. Therefore, [pic]and [pic].
Iteration 2:
Initial guesses are [pic]and [pic]. Again, check requirement: [pic]
[pic], which is ................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
Related searches
- math for year 3
- math for year 4
- free online math for kids
- math for kids 4th grade
- free learning math for adults
- free math worksheets college level
- math worksheets for college students
- math for kids 4th grade for free
- math worksheets college algebra
- math problems for college level
- math for 5th graders worksheets for free
- math test for college entrance