## Calculus Practice Exams

**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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