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Unformatted text preview: x 2 + y 2 ≤ 1. 5. [20pts] The sphere x 2 + y 2 +( z-3) 2 = 9 rests between the two planes x-2 y-2 z = c-x + 2 y-2 z = c. (a) At what points is the sphere tangent to the planes? (b) What is c ? 6. [20pts] We wish to compute the integral Z 1 . 01 . 99 Z 1 . 01 . 99 1 ln2 2-x 2-y 2 dx dy. Because there is no closed form for the antiderivative of the integrand, we must estimate. (a) Find an appropriate linear approximation, L , of the integrand and then integrate L over the region. (b) Find a bound on the error incurred by this estimation. In computing the error bounds, you may use the fact that all second partials of the integrand on the given region have absolute value less than one....
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This note was uploaded on 09/29/2009 for the course 1920 1920 at Cornell.