Introduction, Approximation and Errors

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Introduction, Approximation and Errors
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To find the velocity from acceleration vs time
data, the mathematical procedure used is

• Differentiation
• Integration

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To find velocity from the location vs time data
of the body, the mathematical procedure used is

• Differentiation
• Integration

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Given y sin(2x), dy/dx at x3 is

• 0.9600
• 0.9945
• 1.920
• 1.989

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The form of the exact solution to
is

• .
• .
• .
• .

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Given the f (x) vs x curve, and the magnitude of
the areas as shown, the value of

• -7
• -2
• 12
• Cannot be determined

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A steel cylindrical shaft at room temperature is
immersed in a dry-ice/alcohol bath. A layman
estimates the reduction in diameter by using

• Less
• More
• Same

and uses the value of the thermal expansion
coefficient at room temperature. Seeing the
graph below, the magnitude of contraction you as
an engineer would calculate would be
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The number of significant digits in 0.0023406 is

• 4
• 5
• 6
• 7

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The number of significant digits in 2350 is

• 3
• 4
• 5
• 3 or 4

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The number of significant digits in 2.30500 is

• 3
• 4
• 5
• 6

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The number 6.749832 with 3 significant digits
with rounding is

• 6.74
• 6.75
• 6.749
• 6.750

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The number 6.749832 with 3 significant digits
with chopping is

• 6.74
• 6.75
• 6.749
• 6.750

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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

• 2
• 3
• 4
• 5

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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

• 0.5
• 0.05
• 0.005
• 0.0005

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The error caused by using only a few terms of the
Maclaurin series to calculate ex results mainly
in

• Truncation Error
• Round off Error

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The error caused by representing numbers such as
1/3 approximately is called

• Round-off error
• Truncation error

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(01011)2 (?)10

• 7
• 11
• 15
• 22

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(8)10(?)2

• 1110
• 1011
• 0100
• 1000

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The binary representation of (0.3)10 is

• (0.01001...)2
• (0.10100...)2
• (0.01010...)2
• (0.01100...)2

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In a five bit fixed representation, (0.1)10 is
represented as (0.00011)2. The true error in
this representation most nearly is

• 0.00625
• 0.053125
• 0.09375
• 9.5x10-8

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Smallest 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

• 0.000
• 0.125
• 0.250
• 1.000

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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

• 1.875
• 4
• 7
• 15

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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
exponent

• 0.125
• 0.25
• 0.5
• 1.0

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Taylor series is only valid for

• small values of h
• function and all its derivatives being defined
  and continuous at x
• function and all its derivatives being defined
  and continuous in x,xh

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Five bits are used for the biased exponent. To
convert a biased exponent to an unbiased
exponent, you would

• add 7
• subtract 7
• add 15
• subtract 15