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Unformatted text preview: Practice Problems for the Final, Fall 2006 1. Find the plane that contains the lines L 1 : x = 1+ t, y = 1 − t, z = − t and L 2 : x = 1+3 t, y = − 3 t, z = − 3 − 3 t. 2. Find and classify the critical points of the function f ( x, y ) = 4 x 2 e y − 2 x 4 − e 4 y . 3. Find the absolute maximum of the function f ( x, y, z ) = x 2 yz on the triangle cut by the plane x + y + z = 12 and the first octant. 4. A thin wire lies along the curve r ( t ), 0 ≤ t ≤ 1. The wire density δ (its mass per unit length) increases linearly along the wire and is δ ( r ) = s + 1, where s is the arc length parameter, and s = 0 corresponds to the t = 0 endpoint of the wire. Determine the wire mass if  v ( t )  = t 2 + 1. 5. Consider the gravitational field: F = − GMm ( x i + y j + z k ) ( x 2 + y 2 + z 2 ) 3 / 2 , where G, M, m are constants. (a) Show that the field is conservative. (Hint: Set r = !...
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This test prep was uploaded on 09/23/2007 for the course MATH 1920 taught by Professor Pantano during the Fall '06 term at Cornell.
 Fall '06
 PANTANO
 Critical Point, Multivariable Calculus, Vector Calculus, cylinder x2, Stokes' theorem

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