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11BHW8

# 11BHW8 - at the point x,y =(3 2 Use the Taylor polynomial...

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AMS/ECON 11B SPRING 2008 Homework assignment #8 1. Compute the degree 2 Taylor polynomial for the function f ( x, y ) = x 3 y + 3 x 2 y 2 - 2 xy 2 + 3 x - 5 y, centered at the point ( x 0 , y 0 ) = (1 , 1). 2. Compute the degree 2 Taylor polynomial for the function Q ( K, L ) = 10 K 2 / 3 L 1 / 3 , cen- tered at the point ( K 0 , L 0 ) = (1 , 8). Use the Taylor polynomial that you found to calculate the approximate value of Q (1 . 5 , 8 . 4). 3. Compute the degree 2 Taylor polynomial for the function g ( u, v ) = (2 u + 3 v ) e u 2 + v 2 , centered at the point ( u 0 , v 0 ) = (0 , 0). 4. Compute the degree 2 Taylor polynomial for the function z ( x, y ) = 2 x + 5 y , centered
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Unformatted text preview: at the point ( x ,y ) = (3 , 2). Use the Taylor polynomial that you found to calculate the approximate value of z (3 . 25 , 2 . 1). 5. Compute the degree 2 Taylor polynomial for the function g ( x,y,z ) = 2 ln x + 4 ln y-z (5 x + 8 y-60) , centered at the point ( x ,y ,z ) = (4 , 5 , . 1). 6. Compute the degree 2 Taylor polynomial for the function h ( u,v,w ) = u 2 ( v-2) e u + vw , centered at the point ( u ,v ,w ) = (4 , 2 ,-2)....
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