* Honours Maths Paper 2 " Let's fight back :)

aoifegibney

well this thread is making me feel horrendously unprepared...

epicwinning

Was flicking through an old copy and came across an easy way to do the MacClauren Series for tan-1(x) if anyone else finds that one annoying:

First, differentiate tan-1(x):

d/dx(tan-1(x)) = 1/(1+x^2)

Then use long division to get a few terms for the RHS:



Then integrate both sides:

tan-1(x) = INT[(1) - (x^2) + (x^4) ...]
tan-1(x) = x - (x^3)/3 + (x^5)/5 ...


It's a much easier way of doing that series.

MikeHough

MathsManiac wrote: »

You are correct.

thank you. I thought so.:p

o.d. morris should be ashamed of himself.:pac:

MikeHough

epicwinning wrote: »

Was flicking through an old copy and came across an easy way to do the MacClauren Series for tan-1(x) if anyone else finds that one annoying:

First, differentiate tan-1(x):

d/dx(tan-1(x)) = 1/(1+x^2)

Then use long division to get a few terms for the RHS:



Then integrate both sides:

tan-1(x) = INT[(1) - (x^2) + (x^4) ...]
tan-1(x) = x - (x^3)/3 + (x^5)/5 ...


It's a much easier way of doing that series.

that's the same way as the texts and tests....page 241

epicwinning

Don't have Texts and Tests. We just did it the same way as all the others :P

xxpopopxx

Can anyone please help me out?? For the MacLaurin series how do you get the general term of a series? My teacher only thought us the basics and nothing deeper, I'm freaking out and I keep crying

hairybacon

http://www.mathsireland.com/LCHGeneralNotes/StatsDiffEqns/6_5_Diff_Eqns/Q19_Ans_6_5_Diff_Eqns.html

Can someone explain part b please???

NSNO

For 2007 Q3 (c) (i), would it be correct to state that the given is a line and intersect the two lines and sub the points into the given equation to prove its on the intersection?

You'd get K(0) + L(0) which = 0 as per given, therefore proven it's on the intersection? Because I'm not quite getting the second part of the given answer on the marking scheme. (http://examinations.ie/archive/markingschemes/2007/LC003ALPO00EV.pdf)

joyle

If the SEC want to show how great project maths is by throwing graphs at us, I believe we should brush up on trig graphs and Q8 graph questions too!!

partyatmygaff

joyle wrote: »

If the SEC want to show how great project maths is by throwing graphs at us, I believe we should brush up on trig graphs and Q8 graph questions too!!

Wouldn't it be sweet if they asked us just to draw the graphs of all the trig functions...

dannyirishman

Having a relapse... What is after (N+1)!

Is it (N+1)N!..........(N-1)!

NSNO

partyatmygaff wrote: »

Wouldn't it be sweet if they asked us just to draw the graphs of all the trig functions...

I'd love the 2009 question. Any question which is answerable with "Sin-1(x) is bijective" is a good question.

hunii07

dannyirishman wrote: »

Having a relapse... What is after (N+1)!

Is it (N+1)N!..........(N-1)!

It's (N+1)N!

NSNO

dannyirishman wrote: »

Having a relapse... What is after (N+1)!

Is it (N+1)N!..........(N-1)!

(N+1)! = (N+1)N! = (N+1)(N)(N-1)! = (N+1)(N)(N-1)(N-2)!......

joyle

partyatmygaff wrote: »

Wouldn't it be sweet if they asked us just to draw the graphs of all the trig functions...

or they do like what they did in 06 and 09! would love it

PJelly

Question about getting the general term... say you have the series 1+X+X^2/2!+X^3/3! etc. Do you read 1 as the first term or X as the first term?
And if there's no 1 (as in Ln(1+x)) do you read the X as the first term?
My teacher once mentioned something about reading something as the 0'th term, which I thought made no sense.

epicwinning

xxpopopxx wrote: »

Can anyone please help me out?? For the MacLaurin series how do you get the general term of a series? My teacher only thought us the basics and nothing deeper, I'm freaking out and I keep crying

Step 1: Sign
If there all positive, the U(n) is positive, same with negative.
If it alternates, stick a (-1)^n or (-1)^(n+1) before the gen term.

Step 2: Pattern of x
Find a pattern for the x powers
eg. x, x^2, x^3 add x^n
x, x^3, x^5 add x^(2n-1)

Step 3: Denominator

There should be a similar pattern for the denominator

Step 4: Check with 2 random terms.

joyle

PJelly wrote: »

Question about getting the general term... say you have the series 1+X+X^2/2!+X^3/3! etc. Do you read 1 as the first term or X as the first term?
And if there's no 1 (as in Ln(1+x)) do you read the X as the first term?
My teacher once mentioned something about reading something as the 0'th term, which I thought made no sense.

what ever is the 1st term, read it as the 1st term, whether it be 1 or x

epicwinning

PJelly wrote: »

Question about getting the general term... say you have the series 1+X+X^2/2!+X^3/3! etc. Do you read 1 as the first term or X as the first term?
And if there's no 1 (as in Ln(1+x)) do you read the X as the first term?
My teacher once mentioned something about reading something as the 0'th term, which I thought made no sense.

You could do either to be honest... I'd say let 1 be the first term.

U(n) = [x^(n-1)]/(n-1)!

PJelly

Thanks
My teacher used to say something about not reading one as a term... made no sense to me.
I just got 2005 8 all right too! Progress!
Hopefully things go as smoothly on the day.

xxpopopxx

epicwinning wrote: »

Step 1: Sign
If there all positive, the U(n) is positive, same with negative.
If it alternates, stick a (-1)^n or (-1)^(n+1) before the gen term.

Step 2: Pattern of x
Find a pattern for the x powers
eg. x, x^2, x^3 add x^n
x, x^3, x^5 add x^(2n-1)

Step 3: Denominator

There should be a similar pattern for the denominator

Step 4: Check with 2 random terms.

thank you so much! ill try that

conlufc

dannyirishman wrote: »

Having a relapse... What is after (N+1)!

Is it (N+1)N!..........(N-1)!

ye your right

PJelly

NSNO wrote: »

(N+1)! = (N+1)N! = (N+1)(N)(N-1)! = (N+1)(N)(N-1)(N-2)!......

I just remember that you keep taking off one. And when you want to stop place a factorial (!) on the last one you do.

PJelly

That awkward moment when you manage to spill your tea on every single maths book you own at the same time.

B_Fanatic

epicwinning wrote: »

You could do either to be honest... I'd say let 1 be the first term.

U(n) = [x^(n-1)]/(n-1)!

Is that denominator right? I mean if the first term is one wouldn't n - 1 make it infinity? Or do I just disregard it because factorial doesn't go as far as zero? E.g. 4! =/= 4x3x2x1x0 :rolleyes:

easkey92

what are all d properties for standard deviation and means ?? please help

jamesr1775

PJelly wrote: »

That awkward moment when you manage to spill your tea on every single maths book you own at the same time.

lol pwned!! ahhh well last few hours of using them is left anyway

Digits

B_Fanatic wrote: »

Is that denominator right? I mean if the first term is one wouldn't n - 1 make it infinity? Or do I just disregard it because factorial doesn't go as far as zero? E.g. 4! =/= 4x3x2x1x0 :rolleyes:

0! = 1

PJelly

jamesr1775 wrote: »

lol pwned!! ahhh well last few hours of using them is left anyway

My papers are literally stuck to the table

PJelly

Digits wrote: »

0! = 1

I love scaring the ordinary maths lads by putting 9/0! on the calculator and showing how it equals nine. It's my party trick.