10s.pdf - Math 10C Fall 2010 Final Exam Problem 1 Consider...

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Math 10C - Fall 2010 - Final ExamProblem 1.Consider the functionf(x, y) =x2y-xlny.(i)Find the equation of the tangent plane to the graph offat(2,1,4).(ii)Find a vector normal to the graph off.(iii)Find the quadratic Taylor polynomial offnear the point(2,1).Answer:
Problem 2.Calculate the integralZRxy dx dywhereRis the triangular regionx0, y0, x+ 2y2.
Problem 3.Find the critical points of the functionf(x, y) =xy2-4xy+12x2and determine their nature.

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