Linear Approximation in 2 variables

**Robb** · May 28th 2009, 10:05 PM

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 $x=3.00, y=3.00.$

**Amer** · May 29th 2009, 01:09 AM

$tan^{-1}_x (y/x) =\frac{-y/x^2}{1+(y/x)^2}<br /> <br /> tan^{-1}_y (y/x)=\frac{1/x}{1+(y/x)^2}<br />$

**Amer** · May 29th 2009, 04:12 AM

$f(x,y) = \tan^{-1}\left(\frac{y}{x}\right)<br />$

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

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