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Newton's Method Word Problems
Posted:
Nov 1, 1997 2:19 PM


Thank you all for the very creative word problems using the concepts behind Newton's Method! We certainly are a very creative crowd, aren't we?
I'm afraid that I wasn't all that creative on my last test on 'Applications of the Derivative' which focused on Optimization and Related Rates. So I wrote a quick and dirty Newton's question:
(1) Let f(x) = 1  tan(xpi/2) (a) State the recursive equation describing Newton's Method for Approximating Roots.
(b) Apply this definition to f(x)
(c) Write an equation of the tangent line to f(x) at x0 = pi/2
(d) Use this equation to approximate x1.
(e) Set Mode Fix 9 and use prgmNEWT to create a convergence table with 6 decimal place accuracy starting at x0 given above.
(f) Multiply your best estimate to the first positive root of f(x) by 4/3. State the root exactly.
(g) Make a complete sketch of f(x) and the tangent line at x0. Label x0, x1 and lim n > inf xn on the xaxis.
Other versions of this question can esily be written simply by changing the first line of the equation (for multiple versions of the test, make up exams, etc.). For example: (1) Let f(x) = 1  sin^2(x) (1) Let f(x) = cos^2(x) 1 and the like.
Regards, A. Jorge Garcia  Teacher/Professor AppliedMathematics/ComputerScience BaldwinSHS/NassauCC http://freenet.buffalo.edu/~aj317 mailto:aj317@freenet.buffalo.edu 



