Unformatted text preview: 2) i + ( t − 3) 2 j + ( t − 4) 3 k . a. Suppose that the captain shuts down the engines at time t . ±ind the subsequent motion of the ship. b. Show that if t is chosen appropriately then the ship will hit the beacon. 5 A certain function f ( x, y ) is known to have partial derivatives of the form ∂f ∂x = 2 xy + g ( y ) ∂f ∂y = x 2 + 3 x. Note that g is a function of y only. Use the Clairaut’s Theorem to ²nd the function g up to a constant of integration. Then ²nd all functions f which satisfy these conditions. 6 Rewrite the function f ( x, y ) = x y as a composition of standard functions (hint: think about exponentials and logarithms). Then: a. Determine the domain of f ( x, y ). b. Compute both partial derivatives of f ( x, y ) in its domain....
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 Fall '08
 Keeran
 Calculus, Derivative

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