MA 242 Test 2 Review Sheet (covers 10.3,10.4,11.1-11.7)

 

Section 10.3 Arc Length and Curvature

á   If you need them, I will give you the formulas for N(t), B(t), and k.

á   Examples p. 714: 1,3,5,25

 

Section 10.4 Motion in Space: Velocity and Acceleration

á   Find the velocity, speed, and acceleration given a position vector

á   Find position, velocity, and speed given acceleration

á   Examples p. 725: 5,9,13,15, 21,23,27

 

Section 11.1 Functions of Several Variables:

á   Be able to find the domain of functions of 2 or 3 variables

á   Given a function of 2 variables draw multiple level curves

á   Match a function to its level curves (ex p.749: 35-40)

á   Examples p. 745: 1,5,7,19,21,25

 

Section 11.2 Limits and Continuity:

á   Be able to show a limit does not exist (p.755: 9,13,19)

á   Know the definition of continuity (p.753)

á   Be able to find the limit of a function when it exists (p.755: 5, 6,11,15)

 

Section 11.3 Partial Derivatives:

á   Know ClairautÕs Theorem (p.763)

á   Be able to take partial derivatives

á   Examples p. 767: 3,15, 25,27,35,51,61

 

Section 11.4 Tangent Planes and Linear Approximations:

á   Know how to find the equation of the tangent plane

á   Be able to find a linear approximation to f at a point

á   Understand how the equation for the tangent plane relates to the equation of linear approximation

á   Be able to use differentials to approximate error, volume, etc (p. 778: 31,32,33)

á   Examples p. 778: 1,4,11,17,19

 

Section 11.5 The Chain Rule

á   Understand the different cases of the chain rule (Case 1, Case 2, the General Case)

á   Examples p. 787: 3,5,6,9,13,17,22

 

Section 11.6 Directional Derivatives and the Gradient Vector

á   Be able to find the derivative of f in the direction of a vector v

á   Know how to maximize the directional derivative (p.794 Theorem 15)

á   See the Worksheet on Directional derivatives

á   Examples p. 799: 11,15,19,20, 21,29

 

Section 11.7 Maximum and Minimum Values

á   Know the 2nd Derivative Test (p. 803)

á   Be able to identify local maxs, mins, and saddle points (Refer to the Worksheet on Max/Min)

á   Know how to find absolute maxs and mins on a closed bounded set D (p.808) (See the Worksheet on Absolute Max/Min)

á   Examples p. 809: 1,27,29,30 & p.825: 51,53