we have a polynomial ƒ(x) of degree d is equal to 1 PĄ(x) = f(0) + f'(0)x + " (0)x² + … · +f" (0)x“ . If f is a general function that has dth order derivatives at 0, then the polynomial Pa(x) approximates f(x) for small x. As d increases, these approximations get better, assuming f is a reasonable function. The polynomial P4 is called the degree d Taylor approximation of f at 0. (A) Find the degree 4 Taylor approximations at 0 of cos x. (B) Approximate cos(0.1) using your answer to part (A). For comparison, wolfram alpha tells me cos(0.1) = 0.995004165278.... %3D

we have a polynomial ƒ(x) of degree d is equal to 1 PĄ(x) = f(0) + f'(0)x + " (0)x² + … · +f" (0)x“ . If f is a general function that has dth order derivatives at 0, then the polynomial Pa(x) approximates f(x) for small x. As d increases, these approximations get better, assuming f is a reasonable function. The polynomial P4 is called the degree d Taylor approximation of f at 0. (A) Find the degree 4 Taylor approximations at 0 of cos x. (B) Approximate cos(0.1) using your answer to part (A). For comparison, wolfram alpha tells me cos(0.1) = 0.995004165278.... %3D

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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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

we have
a polynomial f(x) of degree d is equal to
1
1
Pa(x) = f(0) + f'(0)x + "(0)x² + ... +f (0)x“ .
d!-
If f is a general function that has dth order derivatives at 0, then the polynomial P(x)
approximates f(x) for small x. As d increases, these approximations get better, assuming f is a
reasonable function. The polynomial Pa is called the degree d Taylor approximation of f at 0.
(A) Find the degree 4 Taylor approximations at 0 of cos x.
(B) Approximate cos(0.1) using your answer to part (A). For comparison, wolfram alpha tells
me cos(0.1) = 0.995004165278....

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