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tutorial2_sol

# tutorial2_sol - MATH1211/10-11(2/Tu2sol/TNK Department of...

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Unformatted text preview: MATH1211/10-11(2)/Tu2sol/TNK Department of Mathematics, The University of Hong Kong MATH1211 Multivariable Calculus (2010-11 2nd semester) Solution to Tutorial 2 Note : Some solutions given below are outline only. You may need to give more details in your solution. 1. We first find D f ( x,y ) and then plug in ( x,y ) = (1 ,- 1): D f ( x,y ) =    ∂ ∂x (2 x- y ) ∂ ∂y (2 x- y ) ∂ ∂x y 3 ∂ ∂y y 3 ∂ ∂x x sin xy ∂ ∂y x sin xy    =   2- 1 3 y 2 sin xy + xy cos xy x 2 cos xy   , D f (1 ,- 1) =   2- 1 3 sin(- 1)- cos(- 1) cos(- 1)   . 2. The following is a summary of the results. The student should provide some argument to support the answer. E.g., for a point ( a,b ) where both a,b 6 = 0, one can find a δ > 0 such that the open ball centered at ( a,b ) with radius δ contains only points ( x,y ) with x,y 6 = 0, so that f = 0 on this entire open ball. It is then easy to see that f is continuous and differentiable at ( a,b ), and both...
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