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Math Help - Linear Approximation in 2 variables

  1. #1
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    Linear Approximation in 2 variables

    Hello MHF,
    needing some help in computing the following...
    Compute the equation of the tangent plane to the graph of the function
     f(x,y) = \tan^{-1}\left(\frac{y}{x}\right)
    at x=3.00, y=3.00.
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  2. #2
    MHF Contributor Amer's Avatar
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    tan^{-1}_x (y/x) =\frac{-y/x^2}{1+(y/x)^2}<br /> <br />
tan^{-1}_y (y/x)=\frac{1/x}{1+(y/x)^2}<br />
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  3. #3
    MHF Contributor Amer's Avatar
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    Jordan
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    f(x,y) = \tan^{-1}\left(\frac{y}{x}\right)<br />

    f_{x}=\frac{-y/x^2}{1+(y/x)^2}

    f_{y}=\frac{1/x}{1+(y/x)^2}
    linear Approximation

    f(x,y)=f(a,b)+f_{x}(a,b)(x-a)+f_{y}(a,b)(y-b)

    All you have to do now is to substitute (3,3) instead of a,b
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