# Use lagrange multipliers to analyze the function on

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Use Lagrange multipliers to analyze the function on the boundary. Do not neglect the interior of the disk in doing your analysis!!

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TEST3/MAC2313 Page 5 of 5 ______________________________________________________________________ 9. (10 pts.) Reveal all the details in using the substitution u = x / a and v = y / b with a > 0 and b > 0 to evaluate the integral below, where R is the elliptical region defined by x 2 a 2 y 2 b 2 1. [Hint: Remember that such a substitution defines T -1 , not T.] ______________________________________________________________________ 10. (10 pts.) Compute the surface area of the portion of the paraboloid defined by z = 16 - x 2 - y 2 that lies above the xy-plane. ______________________________________________________________________ Silly 10 Point Bonus: Become a polar explorer. Compute the exact value of the double integral where R is the region in the first quadrant bounded by the lines y = x /3 and y = 2 x and the circle centered at the origin with a radius of 2. Say where your work is, for it won’t fit here.
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