Solve these numerical method problems. 1. Consider the function f(x) = -r³ – cos(x).%3Da) 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 p3.2. a) Show that for any positive integer k, the sequence defined by p, =converges linearly to p = 0.b) Show that the sequence defined by p, =p = 0 quadratically.10-n* does not converge to

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1. Consider the function f(z) = -r³ – cos(1). %3D a) Use Newton's method with po = -1 to find p2. Could po = 0? b) Use Secant method with po = -1 and pi = 0 to find p3. 2. a) Show that for any positive integer k, the sequence defined by p, = nverges linearly to p = 0. b) Show that the sequence defined by Pn = 10–n* does not converge to = 0 quadratically.

1. Consider the function f(z) = -r³ – cos(1). %3D a) Use Newton's method with po = -1 to find p2. Could po = 0? b) Use Secant method with po = -1 and pi = 0 to find p3. 2. a) Show that for any positive integer k, the sequence defined by p, = nverges linearly to p = 0. b) Show that the sequence defined by Pn = 10–n* does not converge to = 0 quadratically.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Solve these numerical method problems.

1. Consider the function f(x) = -r³ – cos(x).
%3D
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.
2. a) Show that for any positive integer k, the sequence defined by p, =
converges linearly to p = 0.
b) Show that the sequence defined by p, =
p = 0 quadratically.
10-n* does not converge to

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