Finding the Coefficients of a Taylor Polynomial: A Tricky Integration Question

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Homework Help Overview

The discussion revolves around finding the coefficients of a Taylor polynomial, specifically through the use of Maclaurin series for the functions e-4x and sin(5x). Participants are attempting to understand how to properly combine these series to achieve the desired polynomial form.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the potential to use Maclaurin series for both functions and consider how to combine them. There is uncertainty about whether to multiply series term by term or treat them as polynomials. Some participants question the number of terms needed from each series to achieve the correct degree.

Discussion Status

There is an ongoing exploration of how to correctly multiply the series and what terms to include. Some guidance has been offered regarding the polynomial multiplication approach, but participants are still clarifying their understanding and correcting earlier mistakes.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the methods they can use. There is also a focus on ensuring that only terms up to a certain degree are included in the final polynomial.

izelkay
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Homework Statement


Here's a screenshot of the problem: http://puu.sh/2Bta5


Homework Equations





The Attempt at a Solution


As can be seen by the screenshot, the answer's already given, but I'm not sure how to go about getting it. This one has me stumped since e-4x and sin(5x) are both Maclaurin series that I can easily find. But I'm not sure where to go from there, or if I'm even supposed to use both of the Maclaurin series.
 
Last edited by a moderator:
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izelkay said:

Homework Statement


Here's a screenshot of the problem: http://puu.sh/2Bta5


Homework Equations





The Attempt at a Solution


As can be seen by the screenshot, the answer's already given, but I'm not sure how to go about getting it. This one has me stumped since e-4x and sin(5x) are both Maclaurin series that I can easily find. But I'm not sure where to go from there, or if I'm even supposed to use both of the Maclaurin series.
It looks like you are supposed to write a few terms of the Maclaurin series for e-4x in one area and a few terms for the series for sin(5x) in the other area.
 
Last edited by a moderator:
izelkay said:

Homework Statement


Here's a screenshot of the problem: http://puu.sh/2Bta5


Homework Equations





The Attempt at a Solution


As can be seen by the screenshot, the answer's already given, but I'm not sure how to go about getting it. This one has me stumped since e-4x and sin(5x) are both Maclaurin series that I can easily find. But I'm not sure where to go from there, or if I'm even supposed to use both of the Maclaurin series.

Using both the Maclaurin series is probably the easiest way to do it. Just multiply them together. Ignore products that will give you powers greater than 3.
 
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Dick said:
Using both the Maclaurin series is probably the easiest way to do it. Just multiply them together. Ignore products that will give you powers greater than 3.

Ok, that's what I thought I should do but wasn't sure if that was allowed or not.
Is this correct so far? :

http://puu.sh/2BySD

Mark44 said:
It looks like you are supposed to write a few terms of the Maclaurin series for e-4x in one area and a few terms for the series for sin(5x) in the other area.

I'll try this too, thanks.
 
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izelkay said:
Ok, that's what I thought I should do but wasn't sure if that was allowed or not.
Is this correct so far? :

http://puu.sh/2BySD



I'll try this too, thanks.

No, not correct. You don't multiply series term by term. You multiply them like polynomials. Write out each series up to power x^3 and then foil them. Like polynomials. Drop powers bigger than 3.
 
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Dick said:
No, not correct. You don't multiply series term by term. You multiply them like polynomials. Write out each series up to power x^3 and then foil them. Like polynomials. Drop powers bigger than 3.

Ah, ok. I think I understand now.
 
Never mind, still not getting it. Looking at these series for e^-4x and sin(5x), wouldn't that mean I need 4 terms (n=0 to n=3) for e^-4x to make that 3rd degree, and 2 terms (n=0 to n=1) for sin(5x) to make that 3rd degree?

So for e^-4x I have:
1 - 4x + 8x - (64/6)x3

For sin(5x):
5x + (125/6)x3

FOILing those out and ignoring powers greater than 3, I get:

5x + (125/6)x3 - 20x2 + 40x3

Is there something else I'm doing wrong?
 
izelkay said:
For sin(5x):
5x + (125/6)x3

For sin(5x):

5x - (125/6)x3

Not plus.
 
Ok, never mind, found my error. That + (125/6)x3 should actually be a - (125/6)x3
 
  • #10
Dick said:
For sin(5x):

5x - (125/6)x3

Not plus.

Just caught it. Thanks for your help, much appreciated.
 

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