Unformatted text preview: x 2 + y 2 , x = e u + v , y = u + v . 12) Find the critical points of f ( x,y ) = x 3xy + y 3 . Use the second derivative test to classify them. 13) Use Lagrange Multipliers to ﬁnd the extreme values of f ( x,y ) = xy subject to 4 x 2 + 9 y 2 = 32. Solutions 1) r ( t ) = h 75 2 t,16 t 2 + 75 √ 3 2 t i 2) 1 2 (65 3 / 25 3 / 2 ) 3) 5 4) r ( t ) = h e t ,3 , 1 2 t 2 + t + √ 2 i 5) Horizontal Traces: Ellipses, Vertical Traces: Parabolas 7) (a) 0 (b) d.n.e. 8) z x = 3 e x 2y 2 + 3 xe x 2y 2 (2 x ), z y = 3 xe x 2y 2 (2 y ) 9) z = 1 2 x1 4 y + 1, f (3 . 99 , 4 . 01) ≈ 1 . 9925 10) 4 √ 2 11) 2( e u + v ) e u + v + 2( u + v ) 12) (0 , 0) saddle, (1 / 3 , 1 / 3) local min. 13) 8 / 3 is max.,8 / 3 is min. 1...
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 Fall '07
 BoonYeap
 Derivative, lim, Vertical traces, 75 ft, accelaration vector et

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