Calculus Practice Exams

Time: 1 hour

Problem 1. Find all local maxima and minima of the function


Problem 2. Use the method of Lagrange multipliers to find the point on the line of intersection of the planes


that is the closest to the origin.

Problem 3. Use the method of Lagrange multipliers to find local maxima of


under the constraints


Problem 4. Find the integral of


over the plane region G bounded by the lines y = x, y = -x and x = 4

Problem 5. Evaluate


If you would like to check your answers, click on Answer.

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