Exam 14: Partial Derivatives

Find the differential of the function.

Find the limit if .

At what point is the following function a local maximum?

Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height cm if the tin is 0.04 cm thick.

Determine where the function is continuous.

The ellipsoid intersects the plane in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2).

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.

If use the gradient vector to find the tangent line to the level curve at the point .

Find the shortest distance from the point to the plane .

Find the domain and range of the function .

Find the first partial derivatives of the function .

Find and determine where h is continuous.

Use polar coordinates to find the limit.

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

If and changes from (2, 1) to find dz.

Find the first partial derivatives of the function

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

Find three positive numbers whose sum is and whose product is a maximum.

Use implicit differentiation to find

Determine the largest set on which the function is continuous.