1
Name: __________________________________________
Practice Final Exam G3
Section 1 (2 pts each)
Please answer the questions below by selecting one of the answers provided.
1.
You perform a Taylor series expansion of function around the point
x
=2 and obtain the following
result after keeping the first two terms in the series.
)
2
(
5
10
)
(
−
+
≈
x
x
f
Which of the following functions could have represented the original
f(x)
?
a.
x
x
f
5
10
)
(
−
=
b.
x
x
f
5
10
)
(
+
=
c.
x
x
f
=
)
(
d. None of the above
2.
You have a system of 4 linear equations that you are solving using Gaussian elimination with back
substitution and you end up with the following A matrix and b vector during the elimination process.
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
=
1
.
0
5
.
0
5
.
0
1
1
1
5
0
4
.
0
6
.
0
2
0
2
.
0
3
.
0
1
0
1
.
0
5
.
0
1
2
b
A
Which of the following statements is true:
a.
This system of equations has no solution.
b.
This system of equations has an infinite number of solutions.
c.
This system of equations has a single unique solution.
d.
None of the above.
3.
The presence of a double root in an equation is problematic for bracketed root finding methods
because
a.
The solution for the bracketed method will always diverge outside of the original
bracketed range.
b.
There is no sign change in the function value on either side of the root.
c.
Bracketing methods can not find a root in an interval that contains more than one root.
d.
None of the above.
4.
If you execute the following lines of MATLAB code in a function:
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sum = 0
for point = 3:4
if abs(point) ~= 0 then
sum = sum + point
e
l
s
e
s
u
m
=
0
e
n
d
e
n
d
What will be the numeric value stored in
sum
when this calculation is complete?
a.
0
b
.
1
c.
10
d.
None of the above
5.
Which of the following root finding methods would be most appropriate in that it would likely
converge the fastest for finding the root of the following function
a.
NewtonRaphson
b.
Secant method
c.
Bisection
d.
None of the above
6.
You collect 5 new data points on concentration in a process that has a mean concentration value of
10 moles/L with a population standard deviation of 1.
You set control limits on concentration at 9
moles/L and 11 moles/L.
What is the chance that you will make a type I error about whether the
concentration is within the control limits?
a.
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 Spring '07
 Gallivan
 Boundary value problem, b. c. d., fain, CCout, CAin FBin

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