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anonymous
 5 years ago
Power Series: I'm having trouble understanding the concept. Here is one problem that I need help with:
Find the power series representation for f(x)=(4+x)/(1x)
anonymous
 5 years ago
Power Series: I'm having trouble understanding the concept. Here is one problem that I need help with: Find the power series representation for f(x)=(4+x)/(1x)

This Question is Closed

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1Do we write it out like a polynomial?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1What is your understanding of a power series?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0umm hardly anything at all really. I understand what we are trying to do (at least I think I do) but i dont know how to do it.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1:) from the notes online it looks like it is a "sum" of something... what can you tell me about them.. in general

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sums? that its a sequence with all the numbers being added together. so \[\sum_{n=1}^{\infty} 1/n\] would be (1+1/2+1/3....) and so forth.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1good..good..... what is your gut telling you about this problem?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1I have almost zero concepts about this so your driving.... tell me, how does the derivative help us? We can find the derivative quite easily, but what does that do for us?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0umm I don't know. but it makes it into \[f'(x)= 5/((1x)^2)\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1that is correct for the derivative :) tell me...every time ive seen the big E symbol it was talking about "integration". Would that be any help for us here?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1better yet, is there a problem that you already know how to do that you can step me through?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[f(x)=arccot (x)\] so... the derivative of that: \[f'(x)=1/(1+x^2)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0meaning the integral of f'(x)=f(x)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1usually denoted in the textbooks a F(x) :) but yeah....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and power series f'(x) of that is \[\sum_{n=0}^{\infty} (1)^nx^(2n) \] (that's x raised to the 2n)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the integral of the power series=the power series of f(x)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1so step one, you found the derivative of arccot(x) right? and worked with it?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1then step one here is to find the derivative :) your gut was good....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but I dont know how to deal with the whole being squared instead of just x

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.15/ (1x)^2 would it be better in expanded form? x^2 2x +1 ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no the standard form for the power series i'm dealing with right now is 1/(1x) so i have to manipulate it into that form. The five is easy enough to get rid of by simply factoring it out but the (1x)^2 is harder.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1found this, might help if you understand this stuff :) Example 4 Find a power series representation for the following function and determine its interval of convergence. g(x) = 1/ (1x)^2 Solution....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1Solution To do this problem let’s notice that 1/ (1x)^2 = (d/dx) 1/ (1x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0crap that means i take the derivative again? . thats a double integral.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1lol...hold on its using the d/dx form later on.. might be helpful

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1Then since we’ve got a power series representation for 1/(1x) all that we’ll need to do is differentiate that power series to get a power series representation for

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay i think i see where this is going

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1this might be quicker :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1it was years before I knew what the "PrtScn" button was for... it captures a screenshot that you can psate into "Paint"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah i just figured that out about a year ago myself

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1any of that jargon help you out with this problem?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i think so I let you know shortly if the answer i get is right.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wrong answer but i think i understand the concept better.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1at least one of us does :) good luck
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