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Thread: First Year Mathematics B (Integration, Series, Discrete Maths & Modelling)

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    Ancient Orator leehuan's Avatar
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    Re: MATH1231/1241/1251 SOS Thread





    Part a) was quite ok

    Part b)... what? How does that even work

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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by leehuan View Post




    Part a) was quite ok

    Part b)... what? How does that even work
    Once you apply the substitution, maybe you could differentiate both sides again?

    Edit: nah that's useless.
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

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    Re: MATH1231/1241/1251 SOS Thread

    Just out of curiosity, what's an example of a first order linear ODE that's also exact?

    Or does this not exist

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    Re: MATH1231/1241/1251 SOS Thread



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    Re: MATH1231/1241/1251 SOS Thread

    Of course, an obvious and trivial example would be the ODE 0y + y' = 0, i.e. y' = 0.
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    Re: MATH1231/1241/1251 SOS Thread

    What am I doing wrong in this integration question? Soz it's messy.

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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by Flop21 View Post
    What am I doing wrong in this integration question? Soz it's messy.

    Integral of cos(u) is just sin(u), not (1/u)*sin(u).

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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by InteGrand View Post
    Integral of cos(u) is just sin(u), not (1/u)*sin(u).
    Oh yeah ha whoops thanks.
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    Re: MATH1231/1241/1251 SOS Thread

    How do you differentiate e^x*y^2. ?

    Actually it's a partial derivative with respect to y, but I don't know how to differentiate this one normally anyway.
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by Flop21 View Post
    How do you differentiate e^x*y^2. ?

    Actually it's a partial derivative with respect to y, but I don't know how to differentiate this one normally anyway.






    e^(x*(y^2)).



    (e^x)*(y^2).
    Last edited by InteGrand; 17 Aug 2016 at 12:14 PM.

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    Re: MATH1231/1241/1251 SOS Thread

    How to integrate sec^4 x dx ?
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by Flop21 View Post
    How to integrate sec^4 x dx ?

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    Re: MATH1231/1241/1251 SOS Thread

    Sigh...






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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by leehuan View Post
    Sigh...







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    Re: MATH1231/1241/1251 SOS Thread

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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by InteGrand View Post
    Ah I see. Yeah I was mainly lost in why the roots are specifically 2cos(...) but then I realised |root|=1


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    Re: MATH1231/1241/1251 SOS Thread

    Forgot how to puzzle things together today. Just part e) please








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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by leehuan View Post
    Forgot how to puzzle things together today. Just part e) please







    Suppose by way of contradiction there was a root "a" with |a| > 3.

    Since a is a root, we have

    a^6 = 3a - a^3 + 5a^4.

    Taking modulus of both sides, |a^6| = |3a - a^3 + 5a^4|.

    But this contradicts the result of part d).
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    Re: MATH1231/1241/1251 SOS Thread

    im beyond math help. Dont even know how to integrate, or wtf a matrix is. Or how to diff.s. RIP.
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by Mr_Kap View Post
    im beyond math help. Dont even know how to integrate, or wtf a matrix is. Or how to diff.s. RIP.
    well you can only blame yourself for continuing ur study methods from 1131, need to do a lot of practice in 12X1 especially for new material



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    Re: MATH1231/1241/1251 SOS Thread

    Yeah 1131 started off soft, but 1231 is literally just continuing on so it starts off pretty hard.



    How did they go from here to here:



    Where did 1/3 come from?
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by Flop21 View Post
    Yeah 1131 started off soft, but 1231 is literally just continuing on so it starts off pretty hard.



    How did they go from here to here:



    Where did 1/3 come from?
    Reverse Chain Rule
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by Flop21 View Post
    Yeah 1131 started off soft, but 1231 is literally just continuing on so it starts off pretty hard.



    How did they go from here to here:



    Where did 1/3 come from?


    The integral is the very simple power integral of the form:

    Last edited by Drongoski; 21 Aug 2016 at 8:49 PM.
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    Re: MATH1231/1241/1251 SOS Thread



    The answers said to use induction. Is this really necessary?

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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by leehuan View Post


    The answers said to use induction. Is this really necessary?
    What other method do you have in mind? (Induction helps takes care of it nicely if you want to prove it straight from the axioms.)

    Last edited by InteGrand; 23 Aug 2016 at 10:46 AM. Reason: Typo
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