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Big Willy

Guru

Karma Points: 2,004

(Middle Tennessee State University)

Date Posted: 5/16/2008 11:38:53 AM Status: Live

Asker's Rating: Helpful

Response:

Make a table of derivatives and plug in 2π/3 in for each

f(x) = cos x = 1/2

f'(x) = - sin x = -√3/2

f"(x) = - cos x = -1/2

f"'(x) = sin x = √3/2

f(4) (x) = cos x = 1/2

Write out the series based on the form of a Taylor series

1/2 (x-2π/3)0 + -√3/2 (x-2π/3) + -1/2 (x-2π/3)² + √3/2(x - 2π/3)³ + 1/2 ( x- 2π/3)⁴

0! 1! 2! 3! 4!

I'll be back for the next part; I have to look up Taylor's Inequality and review.

Bpanda

Oracle

Karma Points: 9,099

Date Posted: 5/16/2008 12:25:35 PM Status: Live

Asker's Rating: Lifesaver

Response:

The Taylor series of a function f(x) that is infinitely differentiable in a neighborhood of a number a is the power series: $f(a)+\frac{f'(a)}{1!}(x-a)+\frac{f''(a)}{2!}(x-a)^2+\frac{f^{(3)}(a)}{3!}(x-a)^3+\cdots\,,$

which in a more compact form can be written as

$\sum_{n=0}^{\infin} \frac{f^{(n)}(a)}{n!} (x-a)^{n}\,,$

in our case : a = π/3 and f(x) = cos(x), n = 4

You Don't Mess with the Panda

Bpanda

Oracle

Karma Points: 9,099

Date Posted: 5/16/2008 12:52:08 PM Status: Live

Asker's Rating: Helpful

Response:

(b)

R₄(x) is given by :

we have :

therefore:

thus:

You Don't Mess with the Panda

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please help!!!!

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