Binomial theorem - finding coefficients
Posted 21 January 2006 - 02:12 PM
1. Find the coefficient of x and the term independent of x in the expansion (1/x - x)
What I don't understand is that the two terms in the bracket are both x terms, whereas usually I see (x+y)
2. Just a quick guassian elimination question
is the following applicable for upper triangle form?
n n 0 n
0 n n n
0 0 n n
(where "n" is non-zero number)
it is just that 0 in the first row that is annoying me. I tried a question with the above being the final upper triangular form that I got, but the answer was wrong for me.
I would appreciate any help
Posted 21 January 2006 - 11:48 PM
T in the Park 2008!
Posted 22 January 2006 - 01:46 AM
thank you for offering help
Posted 22 January 2006 - 02:29 AM
that is what
If i am not here i am somewhere else
Posted 22 January 2006 - 02:15 PM
It's ususally just a case of solving the binomial.
Then find the coefficients.
But first I think you need to simplify that 1/x2 - x
Let's see... maybe if you get it out to be:
Did you actually write out Pascal's triangle row for ^18 or did you do it by calculator?
Posted 22 January 2006 - 05:30 PM
So the term in x9 must satisfy 18 - 3r = 9, i.e. r = 3.
You can then find the coefficient by replacing r with 3 in the expression for the general term. I agree with -816 for that.
The method is similar for the term independent of x (this satisfies 18 - 3r = 0). I got 18564.
Posted 22 January 2006 - 06:36 PM
it is to do with graph sketching and asymptotes
to start with the function is f(x) = x / (x - 1)
I used long division to get x + x / (x - 1). So far so good (unless I am wrong )
I worked out the vertical asymptote (x=1) but it is the approach to the graph that I am unsure about. I usually do a table of signs where the top row shows the value of x (values above and below the x=1 -> the asymptote). The next two rows show the numerator and denominator (respectively) of the function. The next row shows the value of the y.
It is the middle two rows that I am unsure about. I can fit the numerator and denominator in, but there is also a ( + x ) part to it and I am unsure where to place this....or should I ignore it?
If you don't understand what I am saying, I will try and explain it more
Posted 22 January 2006 - 08:08 PM
Posted 22 January 2006 - 10:51 PM
Yeh, soz I never included the method. Twas because I didnt know how to write it all in these messages!
T in the Park 2008!
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