- #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)
2. Here is what I did:
p0x = cos (0∏) = 1
p1x = cos(0∏) - ∏sin(0∏)x = 1
p2x = cos(0∏) - ∏sin(0∏)x -[itex]\frac{∏2(cos∏x)(x2)}{2!}[/itex](
and so on...
And the pattern that forms are that the odd values for k are 0.
So p0x = p1x
and p2x = p3x
etc etc.
fk(x) = (∏)kcos(∏x)'
and fk(0) = (∏)k(-1)k
As for the sigma notation:
Here is what I obtained:
Ʃnk = 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 .
cos(∏x)
2. Here is what I did:
p0x = cos (0∏) = 1
p1x = cos(0∏) - ∏sin(0∏)x = 1
p2x = cos(0∏) - ∏sin(0∏)x -[itex]\frac{∏2(cos∏x)(x2)}{2!}[/itex](
and so on...
And the pattern that forms are that the odd values for k are 0.
So p0x = p1x
and p2x = p3x
etc etc.
fk(x) = (∏)kcos(∏x)'
and fk(0) = (∏)k(-1)k
As for the sigma notation:
Here is what I obtained:
Ʃnk = 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 .