# Q9 - Version 057 – DGQ09 – gilbert –(55485 1 This...

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Unformatted text preview: Version 057 – DGQ09 – gilbert – (55485) 1 This print-out should have 3 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find the linearization, L ( x, y ), of f ( x, y ) = x √ y at the point (- 2 , 4). 1. L ( x, y ) = 2 + 2 x- 1 2 y correct 2. L ( x, y ) =- 4 + 1 2 x- y 3. L ( x, y ) =- 2 + 2 x + 1 2 y 4. L ( x, y ) =- 2 + 1 2 x + 2 y 5. L ( x, y ) =- 4 + x + 1 2 y 6. L ( x, y ) = 2- 1 2 x + 2 y Explanation: The linearization of f = f ( x, y ) at a point ( a, b ) is given by L ( x, y ) = f ( a, b )+( x- a ) ∂f ∂x vextendsingle vextendsingle vextendsingle ( a,b ) +( y- b ) ∂f ∂y vextendsingle vextendsingle vextendsingle ( a,b ) . But when f ( x, y ) = x √ y , ∂f ∂x = √ y , ∂f ∂y = x 2 √ y ; thus when ( a, b ) = (- 2 , 4), ∂f ∂x vextendsingle vextendsingle vextendsingle ( a,b ) = 2 , ∂f ∂y vextendsingle vextendsingle vextendsingle ( a,b ) =- 1 2 , while f ( a, b ) =- 4. Consequently,4....
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Q9 - Version 057 – DGQ09 – gilbert –(55485 1 This...

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