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Thread: MATH2111 Higher Several Variable Calculus

  1. #176
    Ancient Orator leehuan's Avatar
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    Re: MATH2111 Higher Several Variable Calculus





    c) Give a simple formula for f(x)

    Last edited by leehuan; 11 Jun 2017 at 10:32 PM.

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    Re: MATH2111 Higher Several Variable Calculus

    Quote Originally Posted by leehuan View Post




    c) Give a simple formula for f(x)

    It won't be -x^3. It'll be a different cubic. It will be an odd cubic that satisfies f(pi) = 0.
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    Ancient Orator leehuan's Avatar
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    Re: MATH2111 Higher Several Variable Calculus

    Quote Originally Posted by InteGrand View Post
    It won't be -x^3. It'll be a different cubic. It will be an odd cubic that satisfies f(pi) = 0.
    Oh, now that I think about it could it potentially be x(x^2-pi^2)?

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    Re: MATH2111 Higher Several Variable Calculus

    Quote Originally Posted by leehuan View Post
    Oh, now that I think about it could it potentially be x(x^2-pi^2)?
    Yeah but the third derivative was negative, so it'd be the negative of what you wrote there.
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    Ancient Orator leehuan's Avatar
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    Re: MATH2111 Higher Several Variable Calculus

    (Stats is done for this sem)




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    Re: MATH2111 Higher Several Variable Calculus

    Quote Originally Posted by leehuan View Post
    (Stats is done for this sem)




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    Ancient Orator leehuan's Avatar
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    Re: MATH2111 Higher Several Variable Calculus

    Quote Originally Posted by InteGrand View Post
    Chain rule was what was on my mind, but I was getting lost at how to use it



    I also started doubting myself, questioning if it's meant to be a Jacobian or just h-dash.


    Unless, the answer is just that Jh(a) = 0 so RHS = 0 as well


    Edit: Uh, nvm, found a gap in my learning.
    Last edited by leehuan; 19 Jun 2017 at 9:33 PM.

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    Ancient Orator leehuan's Avatar
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    Re: MATH2111 Higher Several Variable Calculus

    Found it really hard to work around the wording for this question. Not sure how to properly use the implicit function theorem.



    Not too sure what exactly they want for my matrices (A|B) either

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    Supreme Member seanieg89's Avatar
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    Re: MATH2111 Higher Several Variable Calculus

    Quote Originally Posted by leehuan View Post
    Edit: Uh, nvm, found a gap in my learning.
    What was your end answer?

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    Re: MATH2111 Higher Several Variable Calculus

    Quote Originally Posted by leehuan View Post
    (Stats is done for this sem)



    lel gl with calculus, most aids course



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    Re: MATH2111 Higher Several Variable Calculus

    Quote Originally Posted by seanieg89 View Post
    What was your end answer?
    I thought I had it but I probably didn't. Not sure what I could possibly do next after

    I really don't feel like that should be the final answer either. Any further guidance?

    Quote Originally Posted by RenegadeMx View Post
    lel gl with calculus, most aids course
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    Last edited by leehuan; 20 Jun 2017 at 9:37 AM.

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    Re: MATH2111 Higher Several Variable Calculus

    Quote Originally Posted by leehuan View Post
    I thought I had it but I probably didn't. Not sure what I could possibly do next after

    I really don't feel like that should be the final answer either. Any further guidance?
    Idk what they want you to say with that wording and those assumptions really. Basically it just means that the image of f'(a) is a subspace of the kernel of g'(f(a)), or equivalently that the image of f'(a) is orthogonal to the gradient vector of g at f(a).
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    Ancient Orator leehuan's Avatar
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    Re: MATH2111 Higher Several Variable Calculus

    Figures, should've thought in that direction
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    Re: MATH2111 Higher Several Variable Calculus

    Quote Originally Posted by leehuan View Post
    Figures, should've thought in that direction
    _______________________



    What have you tried so far? Did you try maybe considering the inverse function theorem?

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    Ancient Orator leehuan's Avatar
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    Re: MATH2111 Higher Several Variable Calculus

    Quote Originally Posted by InteGrand View Post
    What have you tried so far? Did you try maybe considering the inverse function theorem?
    That was definitely the starting point, but that just asserted that there exists an open set that is open, not right?

    Image of an open set under a continuous function might not be open

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    Re: MATH2111 Higher Several Variable Calculus

    Quote Originally Posted by leehuan View Post
    Image of an open set under a continuous function might not be open
    Generally this is correct, but consider the implications of f being an invertible (locally) continuous map.
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    Re: MATH2111 Higher Several Variable Calculus

    Quote Originally Posted by leehuan View Post
    That was definitely the starting point, but that just asserted that there exists an open set that is open, not right?
    Also, if V is a subset of U, then f(V) is automatically a subset of f(U) (true for any function and sets (that make sense)).

    (Or maybe you meant that it doesn't state that f(V) is open.)
    Last edited by InteGrand; 20 Jun 2017 at 2:44 PM.

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    Re: MATH2111 Higher Several Variable Calculus

    Quote Originally Posted by InteGrand View Post
    Also, if V is a subset of U, then f(V) is automatically a subset of f(U) (true for any function and sets (that make sense)).

    (Or maybe you meant that it doesn't state that f(V) is open.)
    Yeah the latter lol
    ________________________________

    Just a yes or no answer please because I can't just tell what to use immediately. I know that it converges pointwise to the zero function.



    Because seeing as though it converges pointwise to something continuous I doubt I can use that, and the Weierstrass M-test doesn't even seem relevant.

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    Re: MATH2111 Higher Several Variable Calculus

    Quote Originally Posted by leehuan View Post
    Yeah the latter lol
    ________________________________

    Just a yes or no answer please because I can't just tell what to use immediately. I know that it converges pointwise to the zero function.



    Because seeing as though it converges pointwise to something continuous I doubt I can use that, and the Weierstrass M-test doesn't even seem relevant.
    No
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    Re: MATH2111 Higher Several Variable Calculus


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    Re: MATH2111 Higher Several Variable Calculus

    Quote Originally Posted by leehuan View Post
    Also the first term on your RHS has a mistake/typo (shouldn't have y).

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    Re: MATH2111 Higher Several Variable Calculus

    Quote Originally Posted by leehuan View Post
    chain rule.

    Sent from my GT-I9506 using Tapatalk

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