(a) Sketch an appropriate graph to show that the equation cosx = x² has two solutions, one in x>0 and the other in x< 0. (b) The Maclaurin series for cosx is 1- 2! +... 4! (i) Use the first two non-zero terms to find the two approximate solutions of the equation cosx x. (ii) What are the corresponding approximations if you take the first three non- zero terms? 2n = 1. n= (2n) (2 (ii) Use the Maclaurin series to show that

(a) Sketch an appropriate graph to show that the equation cosx = x² has two solutions, one in x>0 and the other in x< 0. (b) The Maclaurin series for cosx is 1- 2! +... 4! (i) Use the first two non-zero terms to find the two approximate solutions of the equation cosx x. (ii) What are the corresponding approximations if you take the first three non- zero terms? 2n = 1. n= (2n) (2 (ii) Use the Maclaurin series to show that

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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(a) Sketch an appropriate graph to show that the equation cosx = x² has two solutions,
one in x >0 and the other in x< 0.
(b)
The Maclaurin series for cosx is 1-
+...
2!
4!
(i)
Use the first two non-zero terms to find the two approximate solutions of
the equation cosx x.
(ii)
What are the corresponding approximations if you take the first three non-
zero terms?
2n
=1.
(ii)
Use the Maclaurin series to show that
(2n) (2

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