Exam 14: Partial Derivatives

Select the correct Answer: for each question. -Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick.(rounded to the nearest hundredth.)

Find

Find the shortest distance from the point to the plane Select the correct Answer

Find the domain and range of the function

Find

Find and classify the relative extrema and saddle points of the function for and

Select the correct Answer: for each question. -Evaluate the limit.

Select the correct Answer: for each question. -Find the directional derivative of the function at the point in the direction of the unit vector that makes the angle with the positive x-axis.

Let Select the correct Answer

Select the correct Answer: for each question. -Find the limit

Find an equation of the tangent plane to the given surface at the specified point.

How many nth-order partial derivatives does a function of two variables have?

Use Lagrange multipliers to find the maximum value of the function subject to the given constraints.

Select the correct Answer: for each question. -A boundary stripe 2 in.wide is painted around a rectangle whose dimensions are 100 ft by 240 ft.Use differentials to approximate the number of square feet of paint in the stripe.

Find for Select the correct Answer

Find three positive real numbers whose sum is 388 and whose product is as large as possible.

Select the correct Answer: for each question. -Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick.(rounded to the nearest hundredth.)

Find the linearization L(x, y) of the function at the given point. Round theAnswers to the nearest hundredth.

Use Lagrange multipliers to find the maximum and minimum values of the function subject to the constraints