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Learn about approximation and errors in mathematics with Math for College. Explore topics like differentiation, integration, significant digits, sources of error, and binary and floating-point representation.
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INTRODUCTION, APPROXIMATION AND ERRORS http://nm.mathforcollege.com
This rapper’s name is • Tauheed Epps • 2 Chainz • Tity Boi • Kendrick Lamar http://nm.mathforcollege.com
01.01INTRODUCTION http://nm.mathforcollege.com
To find velocity from location vs time data of the body, the mathematical procedure used is • Differentiation • Integration http://nm.mathforcollege.com
The form of the exact solution to is http://nm.mathforcollege.com
y 5 a b 2 c x 7 Given the f (x) vs x curve, and the magnitude of the areas as shown, the value of • -2 • 2 • 12 • Cannot be determined http://nm.mathforcollege.com
A steel cylindrical shaft at room temperature is immersed in a dry-ice/alcohol bath. A layman estimates the reduction in diameter by using 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. • Less • More • Same http://nm.mathforcollege.com
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01.02MEASURINGERRORS http://nm.mathforcollege.com
The number of significant digits in 2350 is • 3 • 4 • 5 • 3 or 4 http://nm.mathforcollege.com
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 http://nm.mathforcollege.com
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% http://nm.mathforcollege.com
01.03SOURCES OF ERROR http://nm.mathforcollege.com
The error caused by representing numbers such as 1/3 approximately is called • Round-off error • Truncation error http://nm.mathforcollege.com
The number 6.749832 with 3 significant digits with rounding is • 6.74 • 6.75 • 6.749 • 6.750 http://nm.mathforcollege.com
The error caused by using only a few terms of the Maclaurin series to calculate ex results mostly in • Truncation Error • Round off Error http://nm.mathforcollege.com
The number 6.749832 with 3 significant digits with chopping is • 6.74 • 6.75 • 6.749 • 6.750 http://nm.mathforcollege.com
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01.04BINARY REPRESENTATION http://nm.mathforcollege.com
(8)10=(?)2 • 1110 • 1011 • 0100 • 1000 http://nm.mathforcollege.com
(01011)2 =(?)10 • 7 • 11 • 15 • 22 http://nm.mathforcollege.com
01.05FLOATING POINT REPRESENTATION http://nm.mathforcollege.com
Using fixed point representation in a computer puts a upper bound on the ________________ in representing a number. • Absolute true error • Relative absolute true error http://nm.mathforcollege.com
Using floating point representation in a computer puts a upper bound on the ________________ in representing a number. • Absolute true error • Relative absolute true error http://nm.mathforcollege.com
The absolute relative true error in a floating point representation using chopping for a number is less than • Machine epsilon • 2-bits used for exponent http://nm.mathforcollege.com
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 http://nm.mathforcollege.com
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