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Thread: MATH2701 Abstract Algebra/Fundamental Analysis

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    Ancient Orator leehuan's Avatar
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    MATH2701 Abstract Algebra/Fundamental Analysis

    Don't need to show me how to do the entire question if it's way too long. Suggestions are plenty





    My starting point was just saying f(x) < integrand being 1/t instead of sint/t, but working backwards it just gave me

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    Re: MATH2701 Abstract Algebra/Fundamental Analysis

    This may help,
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    Re: MATH2701 Abstract Algebra/Fundamental Analysis

    Quote Originally Posted by leehuan View Post
    Don't need to show me how to do the entire question if it's way too long. Suggestions are plenty





    My starting point was just saying f(x) < integrand being 1/t instead of sint/t, but working backwards it just gave me
    You can try using integration by parts.
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    -insert title here- Paradoxica's Avatar
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    Re: MATH2701 Abstract Algebra/Fundamental Analysis

    Quote Originally Posted by leehuan View Post
    Don't need to show me how to do the entire question if it's way too long. Suggestions are plenty





    My starting point was just saying f(x) < integrand being 1/t instead of sint/t, but working backwards it just gave me
    I'm getting O(x⁻¹)

    Differentiating under the integral sign yields:



    Ignore sin x and integrate both sides to obtain an asymptotic...
    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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    Supreme Member seanieg89's Avatar
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    Re: MATH2701 Abstract Algebra/Fundamental Analysis

    Quote Originally Posted by Paradoxica View Post
    I'm getting O(x⁻¹)

    Differentiating under the integral sign yields:



    Ignore sin x and integrate both sides to obtain an asymptotic...
    They are both true, your statement is just weaker. IBP usually gains you stuff when you are analysing oscillatory expressions...if you just look at the size of things via absolute values, you ignore a lot of the "cancellation" that comes from the oscillation. IBP picks this up.

    Edit: Note that you can recover this improvement from your final expression by integrating the leading order term and NOT ignoring the sin. (The remaining terms have size small enough to not matter.) To deal with this leading oscillatory term you still need to use IBP or something similar, and the differentiation under the integral sign has not saved any time.
    Last edited by seanieg89; 28 Jul 2017 at 4:29 PM.
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    Re: MATH2701 Abstract Algebra/Fundamental Analysis

    This was in the final exam and I never figured it out.





    with the hint x + y + z = (x+y)/2 + (x+z)/2 + (y+z)/2

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    -insert title here- Paradoxica's Avatar
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    Re: MATH2701 Abstract Algebra/Fundamental Analysis

    Quote Originally Posted by leehuan View Post
    This was in the final exam and I never figured it out.





    with the hint x + y + z = (x+y)/2 + (x+z)/2 + (y+z)/2
    leehuan likes this.
    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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