document.write( "Question 1075836: Find the linearization of the function f(x,y)=sqrt(152−5x^2−2y^2) at the point (5, -3).
\n" ); document.write( "L(x,y)=
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\n" ); document.write( "Use the linear approximation to estimate the value of f(4.9,−2.9) = \n" ); document.write( "

Algebra.Com's Answer #690712 by Fombitz(32388) $\"\"$ $\"About$

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\n" ); document.write( "where $\"df%2Fdx\"$ and $\"df%2Fdy\"$ are the partial derivatives and are evaluated at ( $\"x%5B0%5D\"$ , $\"y%5B0%5D\"$ ).
\n" ); document.write( "So then,
\n" ); document.write( " $\"f=sqrt%28152-5%2825%29-2%289%29%29=sqrt%289%29=3\"$
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\n" ); document.write( "So then,
\n" ); document.write( " $\"L%28x%2Cy%29=+3-8.33%28x-5%29%2B2%28y-%28-3%29%29+\"$
\n" ); document.write( " $\"L%28x%2Cy%29=-8.33x%2B2y%2B50.65\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"f%28x%2Cy%29=+-8.33%284.9%29%2B2%28-2.9%29%2B5065\"$
\n" ); document.write( " $\"f%28x%2Cy%29=4.033\"$ when the exact value is $\"f%284.9%2C-2.9%29=3.89\"$
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