11 replies to this topic

[YIC]

prelim revision you know

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

[Paul]

For the Binomial Expansion I got the coefficient to be -816, any1 else get this?

[YIC]

could you please show me the method you used?

thank you for offering help

[Dave]

0nnn
00nn
000n

that is what

[Vixus]

could you please show me the method you used?

thank you for offering help

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?

[George]

We have so using the binomial theorem, the general term is:



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.

[YIC]

thanks for the help everyone

[YIC]

I have another question of you don't mind

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

[Steve]

If you are using a table of values, you could always just do it for .

I think this will make it easier to see what's happening.

[YIC]

oh god thanks steve I am such an idiot! I don't know why I needed the function to stay separated for the table. thanks again

[Paul]

could you please show me the method you used?

thank you for offering help

Yeh, soz I never included the method. Twas because I didnt know how to write it all in these messages!

[YIC]

don't worry, it's fine now