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Unformatted text preview: 4 4. [4 marks] Using the definition (formulate it), prove that the set } 2 , 2 : ) , {( 2 ≤ ≤ = + ∈ = x y x R y x S has zero content. 5 5. ( Test bonus question ) Let ) ( 2 x y xf xy u + = . (a) [3 marks] Determine the constant k such that kxy u u y u x y x = − ∂ + ∂ . (b) [1 mark] Find the directional derivative of u at the point (1, 1) in the direction ( 5 4 , 5 3 ) if it is given that 1 ) 1 ( ) 1 ( = ′ = f f . (c) [1 mark] Fill the blanks: “Suppose f is ……………. .….on an ……….……. …………… set S and M f ≤ ∇ ) ( x for every S ∈ x . Then the inequality …………………………………………………… holds for all ” S ∈ b a , (which is a corollary to the Mean Value Theorem). 6...
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 Fall '09
 RomauldStanczak
 Calculus, Parametric equation, Vectorvalued function

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