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Unformatted text preview: 7, f (1 . 3) ≈ 1 . 6, f (4 . 7) ≈ 2 . 6, the absolute maximum value of f is approximately equal to 3.7. 4. (12 marks) Let f ( x, y ) = 6 x 24 x 3 y + y 4 . (a) Compute an equation of the tangent plane to the graph of f at the point P (1 , 1 , 11). (b) Compute the parametric equations of the normal line to the graph of f at P . (c) Find all points on the graph of f where the tangent plane to the graph is horizontal. 5. (10 marks) Let f ( x, y ) = ( xy 2 + x 4 ( x 2 + y 2 ) 3 / 2 if ( x, y ) ± = (0 , 0) if ( x, y ) = (0 , 0) (a) Show that lim ( x,y ) → (0 , 0) f ( x, y ) does not exist. (b) Is f continuous at (0 , 0)? Justify! (c) Use the limit deﬁnition of partial derivatives to compute ∂f ∂x (0 , 0) and ∂f ∂y (0 , 0) or to show that they don’t exist....
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This note was uploaded on 08/23/2008 for the course MATH 150 taught by Professor Hundemer during the Fall '04 term at McGill.
 Fall '04
 HUNDEMER
 Calculus, Limits

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