CSCI/MATH2308

1 Consider the two mathematically equivalent expressions
?(?) = ?(√? + 1 − √?), and ?(?) =
?
(√?+1+√?)
a) Prove that the two expressions are mathematically equivalent.
b) Which of the two expressions can be evaluated more accurately in floating point
arithmetic? Why?
c) Using 4-digit precision, at ? = 500, ?(500) = 10, and ?(500) = 11.17. Which of
these two evaluations is correct? Explain the discrepancy by performing the
computation and analyzing the interim steps. Use an arbitrary precision calculator
such as https://apfloat.appspot.com/.

CSCI/MATH2308
2 Assume that you are solving the quadratic equation ??
2 + ?? + ? = 0, with ? = 1.22,
? = 3.34, and ? = 2.28, using the standard quadratic formula, and using 3-digit
arithmetic with rounding. Use an arbitrary precision calculator such as
https://apfloat.appspot.com/.
a. What is the computed value for ?
2 − 4???
b. What is the exact value for ?
2 − 4???

DETAILED ASSIGNMENT

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