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Unformatted text preview: 4. lim ( x,y ) → (2 ,3) ± 1 x + 1 y ² 2 = 1 36 12. lim ( x,y ) → ( π 2 , ) =2 18. lim ( x,y ) → (2 , 2) x + y4 √ x + y2 = lim ( x,y ) → (2 , 2) ( √ x + y2)( √ x + y +2) √ x + y2 = lim ( x,y ) → (2 , 2) ( √ x + y + 2) = 4 24. lim P → (1 4 , π 2 , 2 ) tan1 ( xyz ) = tan1 ³π 4 ´ 30. (a) All ( x, y ) so that x 23 x + 2 6 = 0 ⇒ ( x2)( x1) 6 = 0 ⇒ x 6 = 2 and x 6 = 1 (b) All ( x, y ) so that y 6 = x 2 40. Along y = kx, k 6 = 0, lim ( x,y ) → (0 , 0) x + y xy = lim x → x + kx xkx = 1 + k 1k ⇒ diferent limits For diferent values oF k , k 6 = 1 ⇒ Limit DNE...
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 Fall '06
 PANTANO
 Math, Calculus, Arc Length, Multivariable Calculus, Harshad number

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