Year 13 Maths Help Thread

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    (Original post by B_9710)
    You just have to know which trig functions are positive and negative in a given interval. Like you just know that for  0\leq x <\pi /2 ,\ \cos x is positive and for  \pi /2 < x \leq  \pi, \ \cos x is negative.
    Damn it was so easy haha, thank you!
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    You can probably tell I haven't done much maths this summer.
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    how can three equations of x+y+z = 0 formed from a matrix give an eigenvector of (p, q, -p-q)?

    Thanks
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    (Original post by Daiblain)
    how can three equations of x+y+z = 0 formed from a matrix give an eigenvector of (p, q, -p-q)?

    Thanks
    Sorry, I either don't understand the question, or I don't think you gave enough information there. I think it's the latter.
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    (Original post by Daiblain)
    how can three equations of x+y+z = 0 formed from a matrix give an eigenvector of (p, q, -p-q)?

    Thanks
    Well all three equations agree if  x=p,  y=q then  p+q+z=0 so of course  z=-p-q .
    Do you notice that there are many solutions you can try, say  \begin{pmatrix} \alpha \\ -\alpha \\ 0 \end{pmatrix} or  \begin{pmatrix} \beta \\ \beta \\ -2\beta \end{pmatrix} . You actually get an eigenplane, and the eigenplane has equation  x+y+z=0 and you can parametrise the plane in anyway you want if you want it in parametric form. All you would do is add any two linearly independent eigenvectors to get it in parametric form.
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    (Original post by RDKGames)
    Sorry, I either don't understand the question, or I don't think you gave enough information there. I think it's the latter.
    (Original post by B_9710)
    Well all three equations agree if  x=p,  y=q then  p+q+z=0 so of course  z=-p-q .
    Do you notice that there are many solutions you can try, say  \begin{pmatrix} \alpha \\ -\alpha \\ 0 \end{pmatrix} or  \begin{pmatrix} \beta \\ \beta \\ -2\beta \end{pmatrix} . You actually get an eigenplane, and the eigenplane has equation  x+y+z=0 and you can parametrise the plane in anyway you want if you want it in parametric form. All you would do is add any two linearly independent eigenvectors to get it in parametric form.
    Sorry, It's my fault Matrix with eigenvalue 5 is (-211)(1-21)(11-2) to give -2x+y+z = 0, x-2y+z =0 and x+y-2z=0I eliminated one variable to make x=y=z because I can't really see it off the bat, making the eigenvector (x,x,x) -> x(1,1,1)With eigenvalue 2 you get(111)(111)(111)to give x+y+z=0all of this was taken off the mei fp2 book, i just didnt understand the eigenvector that goes with the last matrixThanks a bunch!
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    Yeah, the post came out great
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    Term hasn't even started and yet the thread already has 10% of the posts that the Year 12 thread had.

    Speaking of the Year 12 thread, time for me to bump it!
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    Are all summations of the form \sum^{\infty}_{r=1} \frac{1}{ar+b} where a,b \in \mathbb{R} divergent?
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    (Original post by Palette)
    Are all 'things' of the form \sum^{\infty}_{r=1} \frac{1}{ar+b} where a,b \in \mathbb{R} divergent?
    Yes - take out a factor of (1/a) and you get the sum from 1 to infinity of (1/(x+(b/a)) - which is just a shift of the sum of 1/x - which with these limits we know diverges
    (and in the case a=0 you just have an infinite number of '1/b's added together which must diverge)
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    (Original post by ValerieKR)
    Yes - take out a factor of (1/a) and you get the sum from 1 to infinity of (1/(x+(b/a)) - which is just a shift of the sum of 1/x - which we know diverges
    (and in the case a=0 you just have an infinite number of '1/b's added together which must diverge)
    Thanks for the help; do you mind if I add your name to the helpers list?
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    (Original post by Palette)
    Thanks for the help; would you mind if I add your name to the helpers list?
    What responsibility does being one involve?
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    (Original post by ValerieKR)
    What responsibility does being one involve?
    Nothing more than what you're currently doing.
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    (Original post by Palette)
    Nothing more than what you're currently doing.
    Ok - sure
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    How do u integrate 1/x^2+1
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    (Original post by youreanutter)
    How do u integrate 1/x^2+1
    Use sub  x=\tan \theta .
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    (Original post by B_9710)
    Use sub  x=\tan \theta .
    Is that a c4 method?
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    (Original post by youreanutter)
    Is that a c4 method?
    This integral is not expected is C4 but you can still apply normal substitution methods.
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    Do we need to remember the harmonic identities? Or do we get given them in the question?
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    (Original post by jamestg)
    Do we need to remember the harmonic identities? Or do we get given them in the question?
    http://www.mathsnetalevel.com/downlo...ook.pdf#page=8
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    Thanks! I'm sure I printed off this haha, probably stored it away with all my AS work...

    Looks like I'm going to have to get revising
 
 
 
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