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tut6 - 15 2 e 3 x-2 2 y-1 2 if 1 ≤ x ≤ 3 1 ≤ y ≤ 3...

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Math 237 Tutorial 6 Problems 1: Let f ( x, y ) = 1 + sin x + cos y . a) Calculate P 2 , (0 , 0) ( x, y ) of f . b) Use Taylor’s Theorem to show that | f ( x, y ) - L (0 , 0) ( x, y ) | ≤ x 2 + y 2 2 . 2: Let f ( x, y ) = e 2 x - 3 y . Use Taylor’s theorem to show that the error in the linear approx- imation L (2 , 1) ( x, y ) is at most
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Unformatted text preview: 15 2 e 3 [( x-2) 2 + ( y-1) 2 ] if 1 ≤ x ≤ 3, 1 ≤ y ≤ 3. 3: Let f ( x, y ) = 2 x 2 + 2 xy + y 2 . Prove that for any a ∈ R 2 we have f ( x, y ) ≥ L a ( x, y ) for all ( x, y ) ∈ R 2 ....
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