1. Consider the function f(x) = -x³ – cos(x). a) Use Newton's method with po = –1 to find p2. Could po = 0? b) Use Secant method with po = -1 and p1 = 0 to find p3.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
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1. Consider the function f (x) = -x³ – cos(x).
a) Use Newton's method with po
b) Use Secant method with po
-1 to find
-1 and p1
P2. Could
Po
= 0?
0 to find p3.
||
||
1
2. a) Show that for any positive integer k, the sequence defined by pn =
nk
converges linearly to p = 0.
k
b) Show that the sequence defined by Pn =
10-n" does not converge to
p = 0 quadratically.
Transcribed Image Text:1. Consider the function f (x) = -x³ – cos(x). a) Use Newton's method with po b) Use Secant method with po -1 to find -1 and p1 P2. Could Po = 0? 0 to find p3. || || 1 2. a) Show that for any positive integer k, the sequence defined by pn = nk converges linearly to p = 0. k b) Show that the sequence defined by Pn = 10-n" does not converge to p = 0 quadratically.
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