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Unformatted text preview: x = y and x = y 2 . Write the integrals for i i R fdA in two dierent ways a) As a type one region. b) As a type two region. FINAL EXAM NINETY MINUTES 1)(30 points) Let z = f ( x, y ) = x 3 + y 2-y 2 x . Find all critical points of f . 2)(30 points) Use the method of Lagrange multipliers to nd the points on the curve 1 4 x 2 + y 2 = 1, that are closest and furthest from P (1 , 0). 3)(40 points) Let R be the region bounded by the curves x = y 1 3 and y = x 2 . Write the integrals for i i R fdA in two dierent ways a) As a type one region. b) As a type two region....
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