# Its me

## Its me

﻿Chapter 15
1.

Use the contour map ofto estimate the value of f (-3, 3).

2.

Evaluate the limit.

a. b. c. d. e. none of these

3.

Determine the largest set on which the function is continuous.

4.
A cardboard box without a lid is to have a volume of 6,912 . Find the dimensions that minimize the amount of cardboard used.

5.

Find the minimum of the function.

subject to

6.
Find for .

a. 6 b. 2 c. 0 d. -6 e. -2

7.
Use implicit differentiation to find .

8.
Find for .

9.

Find the indicated partial derivative.

10.
The ellipsoid intersects the plane y = 2 in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2).

11.

Use differentials to estimate the amount of metal in a closed cylindrical can that is 13 cm high and 6 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.

Select the correct answer. (rounded to the nearest hundredth.)

a. b. c. d. e.

12.
Use the Chain Rule to find where s = 3, t = 0.

13.

Find the directional derivative of the function at the given point in the direction of the vector v.

14.

Find the direction in which the maximum rate of change ofat the given point occurs.

a. b. c. d. e.

15.

Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is 96.

16.

Find the equation of the tangent plane and the normal line to the given surface at the specified point

, (1, 1, 4)

17.
If , use the gradient vector to find the tangent line to the level curve...