INTRODUCTION,
APPROXIMATION
AND ERRORS
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01.01
INTRODUCTION
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To find velocity from acceleration vs
time data, the mathematical
procedure used is
A. Differentiation
B. Integration
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A.
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B.
The form of the exact solution to
A.
B.
C.
D.
.
.
.
.
2
dy
+ 3 y = e − x , y (0) = 5
dx
is
Ae −1.5 x + Be − x
Ae −1.5 x + Bxe − x
Ae1.5 x + Be − x
Ae1.5 x + Bxe − x
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A.
0%
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B.
C.
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D.
Given the f (x) vs x curve, and the magnitude
of the areas as shown, the value of
b
∫ f ( x)dx
0
A.
B.
C.
D.
-2
2
12
Cannot be
determined
y
5
a
b
2
c
x
7
25%
A.
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25%
25%
B.
C.
25%
D.
A steel cylindrical shaft at room temperature is
immersed in a dry-ice/alcohol bath. A layman
estimates the reduction in diameter by using
A. Less
B. More
C. Same
∆D = Dα∆T
while using the value of the thermal expansion
coefficient at -108oF.
Seeing the graph below, the magnitude of
contraction you as a USF educated engineer
would calculate would be ______________than
the layman’s estimate.
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END
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01.02
MEASURING
ERRORS
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The number of significant digits in 2.30500 is
A.
B.
C.
D.
3
4
5
6
0%
A.
0%
0%
B.
C.
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0%
D.
The absolute relative approximate error in an iterative
process at the end of the tenth iteration is 0.007%. The
least number of significant digits correct in the answer is
A.
B.
C.
D.
2
3
4
5
0%
A.
0%
0%
B.
C.
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0%
D.
Three significant digits are expected to be correct after an
iterative process. The pre-specified tolerance in this case
needs to be less than or equal to
A.
B.
C.
D.
0.5%
0.05%
0.005%
0.0005%
0%
A.
0%
0%
B.
C.
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D.
01.03
SOURCES OF
ERROR
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The error caused by representing numbers such as 1/3
approximately is called
A. Round-off error
B. Truncation error
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A.
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B.
The number 6.749832 with 3 significant digits with
rounding is
A.
B.
C.
D.
6.74
6.75
6.749
6.750
0%
A.
0%
0%
B.
C.
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0%
D.
The error caused by using only a few terms of the
Maclaurin series to calculate ex results mostly in
A. Truncation Error
B. Round off Error
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A.
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0%
B.
The number 6.749832 with 3 significant digits with
chopping is
A.
B.
C.
D.
6.74
6.75
6.749
6.750
0%
A.
0%
0%
B.
C.
http://numericalmethods.eng.usf.edu
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D.
END
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01.04
BINARY
REPRESENTATION
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(8)10=(?)2
A.
B.
C.
D.
1110
1011
0100
1000
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A.
0%
0%
B.
C.
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D.
The binary representation of (0.3)10 is
A.
B.
C.
D.
(0.01001……...)2
(0.10100……...)2
(0.01010……...)2
(0.01100……...)2
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A.
0%
0%
B.
C.
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D.
01.05
FLOATING POINT
REPRESENTATION
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Smallest positive number in a 7 bit word where 1st bit is
used for sign of number, 2nd bit for sign of exponent, 3
bits for mantissa and 2 bits for exponent
A.
B.
C.
D.
0.000
0.125
0.250
1.000
0%
A.
0%
0%
B.
C.
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0%
D.
Five bits are used for the biased exponent. To
convert a biased exponent to an unbiased
exponent, you would
A.
B.
C.
D.
add 7
subtract 7
add 15
subtract 15
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A.
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B.
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0%
C.
0%
D.
END
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01.07
TAYLOR SERIES
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Taylor series
f ( x + h ) = f ( x ) + f ′( x )h +
f ′′( x ) 2 f ′′′( x ) 3
h +
h +
3!
2!
is only valid
A. if values of h are small
B. if function and all its
derivatives are defined
and continuous at x
C. if function and all its
derivatives are defined
and continuous in [x,x+h]
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A.
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B.
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C.
END
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EXTRA QUESTIONS
http://numericalmethods.eng.usf.edu
(01011)2 =(?)10
A.
B.
C.
D.
7
11
15
22
0%
A.
0%
0%
B.
C.
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0%
D.
The machine epsilon in a 7 bit number where 1st bit
is used for sign of number, 2nd bit for sign of
exponent, 3 bits for mantissa and 2 bits for
25%
25%
25% 25%
exponent
A.
B.
C.
D.
0.125
0.25
0.5
1.0
A.
B.
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C.
D.
The number of significant digits in 0.0023406 is
A.
B.
C.
D.
4
5
6
7
0%
A.
0%
0%
B.
C.
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0%
D.
The number of significant digits in 2350 is
A.
B.
C.
D.
3
4
5
3 or 4
0%
A.
0%
0%
B.
C.
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D.
To find velocity from location vs time
data of the body, the mathematical
procedure used is
A. Differentiation
B. Integration
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A.
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B.
Given y= sin(2x), dy/dx at x=3 is
1.
2.
3.
4.
0.9600
0.9945
1.920
1.989
0%
1
0%
0%
2
3
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0%
4
In a five bit fixed representation, (0.1)10 is
represented as (0.00011)2. The true error in this
representation most nearly is
A.
B.
C.
D.
0.00625
0.053125
0.09375
9.5x10-8
0%
A.
0%
0%
B.
C.
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0%
D.
Largest positive number in a 7 bit number where 1st bit is
used for sign of number, 2nd bit for sign of exponent, 3 bits
for mantissa and 2 bits for exponent
A.
B.
C.
D.
1.875
4
7
15
0%
A.
0%
0%
B.
C.
http://numericalmethods.eng.usf.edu
0%
D.