- #1

Mosaness

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**1. Find the Maclaurin polynomials of order n = 0, 1, 2, 3, and 4, and then find the nth MacLaurin polynomials for the function in sigma notation.**

cos(∏x)

cos(∏x)

**2. Here is what I did:**

p

p

p

p

_{0}x = cos (0∏) = 1p

_{1}x = cos(0∏) - ∏sin(0∏)x = 1p

_{2}x = cos(0∏) - ∏sin(0∏)x -[itex]\frac{∏^{2}(cos∏x)(x^{2})}{2!}[/itex](and so on...

And the pattern that forms are that the odd values for k are 0.

So p

_{0}x = p

_{1}x

and p

_{2}x = p

_{3}x

etc etc.

f

^{k}(x) = (∏)

^{k}cos(∏x)'

and f

^{k}(0) = (∏)

^{k}(-1)

^{k}

As for the sigma notation:

Here is what I obtained:

Ʃ

^{n}

_{k = 0}([itex]\frac{(∏

^{2k}(-1)

^{k}}{k!}[/itex](x)

^{2k}

According to the solution manual however, there is a n/2 on top of the sigma notation instead of a n.

I don't understand .