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Unformatted text preview: x 2 4 + y 2 9 + z 2 25 = 1 does not intersect the plane 15 x10 y +3 z = 90. Find the point on the ellipsoid closest to the plane and ±nd the point on the ellipsoid farthest from the plane. 4. (15 points) Find the mass of the thin plate covering the region R between the curves y = √ 2x 2 , y = √ 1x 2 and y = 0 if the density is δ ( x, y ) = e x 2 + y 2 . 5. (15 points) Compute the volume of the region bounded by the following inequalities: ≤ x ≤ 2 ≤ y ≤ p 4x 2 x 2 + y 2 ≤ z ≤ 4 . 6. (20 points) Consider the region R bounded by the following inequalities: ≤ y 2 cos( θ ) ≤ r ≤ 4 ≤ z ≤ ky, such that k ≥ 4 . For what k is the volume of R equal to 100?...
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This note was uploaded on 06/01/2008 for the course MATH 1920 taught by Professor Pantano during the Spring '06 term at Cornell.
 Spring '06
 PANTANO
 Math

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