Exam 14: Partial Derivatives

Find the limit

Find the differential of the function

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

Find equations for the tangent plane and the normal line to the surface with equation at the point

Use implicit differentiation to find

The height of a hill (in feet) is given by where x is the distance (in miles) east and y is the distance (in miles) north of your cabin.If you are at a point on the hill 1 mile north and 1 mile east of your cabin, what is the rate of change of the height of the hill (a) in a northerly direction and (b) in an easterly direction?

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

If use the gradient vector to find the tangent line to the level curve at the point Select the correct Answer

Use implicit differentiation to find

Let Select the correct Answer

Use the equation to find

Find the differential of the function

Let Find Select the correct Answer

Find the directional derivative of the function at the point in the direction of the unit vector that makes the angle ith the positive x-axis.Select the correct Answer

Use the definition of partial derivatives as limits to find if

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.

Use implicit differentiation to find

Select the correct Answer: for each question. -Find the domain and range of the function

Suppose that over a certain region of space the electrical potential V is given by Find the rate of change of the potential at in the direction of the vector Select the correct Answer

Select the correct Answer: for each question. -Find three positive numbers whose sum is and whose product is a maximum.