Re: limits help

On 23 Oct, 23:30, Alois Steindl <Alois.Stei...@xxxxxxxxxxxx> wrote:
charlescalculus_robertobag...@xxxxxxxxxxx writes:
Hi,

I've been trying to expand the following using series : y = x(1+ e^-
x) / (1 - e^-x). I've tried just about everything, from expanding e^-x
using taylor expansion, to expanding the denominator in the fraction
using the binomial theorem, but nothing seems to work. Can anyone
offer some help? Thanks.

Sincerely,
benjamin

Hello,
you might have to try harder!
If you really need help, you should tell us more about the
circumstances: Is it homework? What are you supposed to do? (e.g. at which
point would you asked to perform the series expansion?) And what
are you supposed to know already?
I would guess, that this is some homework, after you learned Taylor
series and did some similar examples in school. Have a look at these
examples, try to solve them without help!
Another hint: Multiply both the nominator and the denominator with
e^(x/2), do you recognize the fraction?

Alois

--
Alois Steindl,                           Tel.: +43 (1) 58801 / 32558      
Inst. for Mechanics and Mechatronics     Fax.: +43 (1) 58801 / 32598
Vienna University of Technology,         A-1040 Wiedner Hauptstr. 8-10  

Hi, thanks for the help. I see what you mean, when i multiply both the
numerator and denominator by e^(x/2) the function y becomes the
function hyperbolic cotangent x multiplied by x. After checking
wikipedia on the series expansion of y = coth x and multiplying it by
x, i now see why the terms containing the odd powers of x disappear.

However, where did you get the idea of multiplying both the top and
bottom of the fraction by e^(x/2)? Thanks.
.

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