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Topic: Newton's Method Word Problems
Replies: 0

 Alvar J. Garcia Posts: 304 Registered: 12/6/04
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(x-pi/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 x-axis.

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
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