.(a) In the 3 Significant Decimal Digits, Rounding system, Floating Point Number System, compute the midpoint of the interval [a,b] = [0.651, 0.653] using the formula xmid* = (a + b) / 2.00. Make sure that the value of (a + the
.(a) In the 3 Significant Decimal Digits, Rounding system, Floating Point Number System, compute the midpoint of the interval [a,b] = [0.651, 0.653] using the formula xmid* = (a + b) / 2.00. Make sure that the value of (a + the
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![.(a) In the 3 Significant Decimal Digits,
Rounding system, Floating Point Number
System, compute the midpoint of the interval
[a,b] = [0.651, 0.653] using the formula Xmid* =
(a + b) / 2.00. Make sure that the value of (a +
b) is a valid number in this Floating Point
Number System before you divide by 2.00.
That is, Xmid* = fl(fl(a + b) / 2.00).
(b) What is the true value Xmid of the midpoint?
(c) For the value of xmid* from part (a) above,
compute the error in xmid*, the relative error in
Xmid*, and the percent error in xmid*.
(d) Compute the value xmid* of the midpoint
using the formula Xmid* = a + (b − a) / 2, that is,
Xmid* = fl(a + fl(fl(b − a) / 2.0)) .
Is this result any more accurate than the result
in part (a)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a6376af-076b-46db-ad44-654584889b97%2Fbd00be72-0864-4d13-ba74-fd4c4a2807b3%2F8llg3sq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:.(a) In the 3 Significant Decimal Digits,
Rounding system, Floating Point Number
System, compute the midpoint of the interval
[a,b] = [0.651, 0.653] using the formula Xmid* =
(a + b) / 2.00. Make sure that the value of (a +
b) is a valid number in this Floating Point
Number System before you divide by 2.00.
That is, Xmid* = fl(fl(a + b) / 2.00).
(b) What is the true value Xmid of the midpoint?
(c) For the value of xmid* from part (a) above,
compute the error in xmid*, the relative error in
Xmid*, and the percent error in xmid*.
(d) Compute the value xmid* of the midpoint
using the formula Xmid* = a + (b − a) / 2, that is,
Xmid* = fl(a + fl(fl(b − a) / 2.0)) .
Is this result any more accurate than the result
in part (a)?
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