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Math 481a Midterm #1. October 14, 2005
Attention! Please, note that this is the closed book test. You are allowed to use a graphing calculator
(but not a palm). In multiple choice, guessing is not penalized. In other problems, please, show all important
steps in you solution.
1a. (5pt) Suppose that the sequence {n} converges to the limit . In the expression
n   k(n),
the quantity k(n) is called
the convergence;
the absolute error of approximation;
the order of convergence;
the rate of convergence;
the asymptotic error constant.
1b. (5pt) In the proof of Theorem 2.5 about the convergence of Newton's method:
Theorem 2.5: Let f C2
[a, b]. If p [a, b] is such that f(p) = 0 and f (p) = 0, then there exists
a > 0 such that Newton's method generates a sequence {pn}
