e^{b/x}\ =\ e^{bx^{-1}} which is much like the form e^{x^{2}}
So if my assumptions are right,
g(x) = \frac{1}{x^5 ( e^{b/x} -1)}
Is going to be equal to the series representation of x^{-5} times the series representation of /frac{1}{e^{bx^{-1}}}
that being said, I could...
Here is an example of one that I've done before
Isn't this similar to how I find the taylor polynomial for
g(x) = \frac{1}{x^5 ( e^{b/x} -1)}
http://img509.imageshack.us/img509/1417/fasdfci8.jpg
Ok so this is what I've drawn up based on the last post.
T_{n}(\lambda)\ =\frac{f^{(n)}(0)}{n!}\lambda^{n}\ = f(0)+\frac{f^{1}(0)}{1!}x+\frac{f^{2}(0)}{2!}x^{2} +...\frac{f^{n}(0)}{n!}x^{n}
From a few posts ago, f(x) = \frac{1}{x^5 ( e^{a/x} -1)}
So to find the first part of...
Its a calculus 253 course. I need to use a Taylor series approximation of Planck's law to closely match the results of Rayleigh-Jeans law.
assuming f(\lambda)\ =\frac{1}{x^5 ( e^{a/\lambda} -1)}
Then T_{n}(\lambda)\ =\frac{f^{(n)}(0)}{n!}\lambda^{n}\ =...
I feel like I'm getting misunderstood on my basic question.
In the book, it asks: find the taylor polynomial T_{n}(x) for the function f at the number a, then it gives us f(x) = sin x a= pi/6, n=3
another example is f(x) = e^x a=2 and n=3, or f(x)=xe^(-2x) a=0 n=3
assuming my f(x) =...
I'm just so lost. To see if I can clarify things, I'm going to find n derivatives of f(x) = \frac{1}{x^5 ( e^{kx}-1) }, evaluate them at f(0), then calculate my T_{n} values?
To do that, is e^{x}\ =\sum^{\infty}_{n=0}\frac{x^{n}}{n!} going to be useful?
The trouble I'm having is stemming from the Taylor approximation being defined as f(\lambda)\ =\frac{f^{(n)}(a)}{n!}(\lambda-a)^{n} I don't understand what a I should use as the center "a" to start the approximation.
I assume by this you mean that I will only need to find T_{2} which would be...
Based on the information in the textbook, the Maclaurin series for e^x is sum from 0 to infinity of x to the n over n factorial. that being said, I don't know if that's the same as its Taylor series.
e^{hc/\lambda kT}\ =\sum^{\infty}_{n=0}\frac{[\frac{hc}{\lambda kT}]^{n}}{n!} like e^{x}\...