ncr register introduction, approximation and errors

NCR Register

http://nm.mathforcollege.com


INTRODUCTION, APPROXIMATION

AND ERRORS


Identify the picture of your instructor

A. B. C. D.

25% 25%25%25%A.

B.

C.

D. 7


01.01INTRODUCTION


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

A. B.

0%0%

A. DifferentiationB. Integration


To find velocity from acceleration vs time data, the mathematical procedure used is

A. B.

0%0%

A. DifferentiationB. Integration


The form of the exact solution to

A. B. C. D.

0% 0%0%0%

xx BeAe 5.1

xx BxeAe 5.1

xx BeAe 5.1

xx BxeAe 5.1

5)0(,32 yeydxdy x is

A. B. C. D.


Given the f (x) vs x curve, and the magnitude of

the areas as shown, the value of

A. B. C. D.

0% 0%0%0%

b

dxxf0

)(

y

xa5

7

2b c

A. -2B. 2C. 12D. Cannot be determined


Given y= sin(2x), dy/dx at x=3 is

A. B. C. D.

0% 0%0%0%

A. 0.9600B. 0.9945C. 1.920D. 1.989


A. B. C.

0% 0%0%

TDD

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.

A. LessB. MoreC. Same

END



01.02MEASURING

ERRORS


The number of significant digits in 2.30500 is

A. B. C. D.

0% 0%0%0%

A. 3B. 4C. 5D. 6

7


The number of significant digits in 0.0023406 is

A. B. C. D.

0% 0%0%0%

A. 4B. 5C. 6D. 7


The number of significant digits in 2350 is

A. B. C. D.

0% 0%0%0%

A. 3B. 4C. 5D. 3 or 4


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.

0% 0%0%0%

A. 2B. 3C. 4D. 5

7


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% 0%0%0%

A. 0.5%B. 0.05%C. 0.005%D. 0.0005%


01.03SOURCES OF

ERROR

Dreaming



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

A. B.

0%0%

A. Round-off errorB. Truncation error


The number 6.749832 with 3 significant digits with rounding is

A. B. C. D.

0% 0%0%0%

A. 6.74B. 6.75C. 6.749D. 6.750


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

A. B.

0%0%

A. Truncation ErrorB. Round off Error


The number 6.749832 with 3 significant digits with chopping is

A. B. C. D.

0% 0%0%0%

A. 6.74B. 6.75C. 6.749D. 6.750

END



01.04BINARY

REPRESENTATION

This is what you have been saying about your TI-30Xa


A. B. C. D.

0% 0%0%0%

A. I don't care what people say The rush is worth the priceI pay I get so high when you're with meBut crash and crave you when you are away

B. Give me back now my TI89Before I start to drink and whine TI30Xa calculators make me cryIncarnation of of Jason will you ever die

C. TI30Xa – you make me forget the high maintenance TI89.

D. I never thought I will fall in love again!


(8)10=(?)2

A. B. C. D.

0% 0%0%0%

A. 1110B. 1011C. 0100D. 1000


(01011)2 =(?)10

A. B. C. D.

0% 0%0%0%

A. 7B. 11C. 15D. 22


The binary representation of (0.3)10 is

A. B. C. D.

25% 25%25%25%A. (0.01001……...)2

B. (0.10100……...)2

C. (0.01010……...)2

D. (0.01100……...)2


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.

25% 25%25%25%A. 0.00625B. 0.053125C. 0.09375D. 9.5x10-8


01.05FLOATING POINT

REPRESENTATION


Using fixed point representation in a computer puts a upper bound on the ________________ in representing a number.

A. B.

50%50%

A. Absolute true errorB. Relative absolute

true error


Using floating point representation in a computer puts a upper bound on the ________________ in representing a number.

A. B.

50%50%

A. Absolute true errorB. Relative absolute

true error


The absolute relative true error in a floating point representation using chopping for a number is less than

A. B.

50%50%

A. Machine epsilonB. 2-bits used for exponent


The smallest positive number in a 7 bit word where 1st bit is used for the sign of number, 2nd bit is used for the sign of exponent, next 3 bits are used for the magnitude of the mantissa and the last 2 bits are used for the magnitude of the exponent is __________.

A. B. C. D.

0% 0%0%0%

A. 0.000B. 0.125C. 0.250D. 1.000


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

A. B. C. D.

25% 25%25%25%A. add 7B. subtract 7C. add 15D. subtract 15


The largest positive number in a 7 bit word where 1st bit is used for the sign of number, 2nd bit is used for the sign of exponent, next 3 bits are used for the magnitude of the mantissa and the last 2 bits are used for the magnitude of the exponent is _________

A. B. C. D.

0% 0%0%0%

A. 1.875B. 4C. 7D. 15


The machine epsilon in a 7 bit word where 1st bit is used for the sign of number, 2nd bit is used for the sign of exponent, next 3 bits are used for the magnitude of the mantissa and the last 2 bits are used for the magnitude of the exponent is _________

A. B. C. D.

0% 0%0%0%

A. 0.125B. 0.25C. 0.5D. 1.0

END



01.07TAYLOR SERIES


Taylor series (given below) is only valid

A. B. C.

0% 0%0%

32

!3!2hxfhxfhxfxfhxf

A. if values of h are smallB. 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]

END



What will Maury Povich say when he dies, goes to heaven, and sees God?

A. B. C. D.

0% 0%0%0%

A. Why am I here; I should be with the lawyers.

B. Is Connie here?C. You are the Father.D. You are not the father.

I walk like a pimp – Jeremy Reed

You know it's hard out here for a pimp,When he tryin’ to get this money for the rent, For the Cadillacs and gas money spent

ncr register introduction, approximation and errors

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