a6 - The magnitude of each second partial derivative of f...

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Math 237 Assignment 6 Due: Friday, Oct 29th 1. Let f ( x, y ) = e - 2 x + y . Use Taylor’s theorem to show that the error in the linear approximation L (1 , 1) ( x, y ) is at most 6 e [( x - 1) 2 + ( y - 1) 2 ] if 0 x 1 and 0 y 1. 2. Consider f : R 2 R defined by f ( x, y ) = 2 x 2 + 3 y 2 . Prove that for any ( a, b ) R 2 we have f ( x, y ) L ( a,b ) ( x, y ) for all ( x, y ) R 2 . 3.
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Unformatted text preview: The magnitude of each second partial derivative of f is less than 2, for all ( x, y ) within 1 / 4 of (0 , / 4). Find an upper bound for the error in the linear approximation L (0 ,/ 4) ( x, y ) of f for all ( x, y ) within 1 / 4 of (0 , / 4)....
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