2017 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 10
Problem
Newton’s method applied to the equation takes the form of the iteration
(a) What are the roots of ?
(b) Study the behavior of the iteration when to conclude that the sequence
approaches the same root as long as you choose
. It may be helpful to start with the case
.
(c) Assume . For what number
does the sequence always approach
?
(d) For the sequence may approach either of the roots
. Can you find an (implicit) expression that can be used to determine limits
and
such that if
then the sequence approaches
. Hint:
and
approaches
when
becomes large.
Solution
See also
2017 UNM-PNM Contest II (Problems • Answer Key • Resources) | ||
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