Exam 14: Partial Derivatives

Find the second partial derivatives of the function

Use polar coordinates to find the limit.

Use the definition of partial derivatives as limits to find

Use the definition of partial derivatives as limits to find if Select the correct Answer

Find Select the correct Answer

Find the indicated partial derivative.

Use the linearization L(x, y) of the function.

Find the limit Hint: If and if and only if

Find all the second partial derivatives.

The length l, width w and height h of a box change with time.At a certain instant the dimensions are nd l and w are increasing at a rate of 10 m/s while h is decreasing at a rate of 1 m/s.At that instant find the rates at which the surface area is changing.

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

Select the correct Answer: for each question. -If use the gradient vector to find the tangent line to the level curve at the point

Find the first partial derivatives of the function

Find all the saddle points of the function.

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 the dimensions of the rectangular box with largest volume if the total surface area is given as

Find the domain and range of the function

Find the limit.

Find the points on the surface that are closest to the origin.

Select the correct Answer: for each question. -If R is the total resistance of three resistors, connected in parallel, with resistances then If the resistances are measured in ohms as with a possible error of 0.8% in each case, estimate the maximum error in the calculated value of R.