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Math Help - evaluate z

  1. #1
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    evaluate z

    Hello,
    Please try to solve this question.
    Thanks.
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  2. #2
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    The question is asking in other words, does there exists a function z=f(x,y).

    So that, \nabla f(x,y) = e^x \sin y \bold{i} + e^x \cos y \bold{j}

    We need that,
    \frac{\partial f}{\partial x} = e^x \sin y

    \frac{\partial f}{\partial y} = e^x \cos y

    To see if this if this is possible we can use the "cross-partials test". Or just assume that it is possible and see if we arrive at a result, which is what I am going to do.

    The first partial differencial equation solves to:
    f = e^x \sin y + g(y)

    But that means if we differenciate to respect to y:
    \frac{\partial f}{\partial y} = e^x \cos y + g'(y) = e^x \cos y

    So g'(y) = C will work for any constant. We can just choose C=0.

    Thus, f(x,y) = e^x \sin y is a function which works.
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  3. #3
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    another way

    there is another way to solve the problem
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  4. #4
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    Quote Originally Posted by curvature View Post
    there is another way to solve the problem
    I think you did the wrong problem.
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  5. #5
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    Quote Originally Posted by ThePerfectHacker View Post
    I think you did the wrong problem.
    Sorry I uploaded the wrong image. It has been replaced by the correct one.
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