Homework:  Read Sections 12.1-12.5, and work the following problems. You should work all of the problems, since any of them may appear on the midterm. But you will only be handing in the problems marked with an asterisk (*). (These will be due on Tuesday Oct. 3).

• Section 11.5:   5,10,19,24*,75,85* (you should have already worked these problems by now, but note the problems you will turn in on Oct. 3).
• Section 12.1:   11, 17, 22, 45-48,54*,57,64,73*,77
• Section 12.2:   15,17,18,19*,24,29*,33,49,50,51
• Section 12.3:   5, 9, 30*, 47, 79, 80*, 87
• Section 12.4:   1, 11, 17, 22*, 25, 32*, 35

Key Skills :

1. Find the arc length of a space curve.
2. Find the arc length function of a space curve.
3. Rewrite a smooth curve as a function of its arc length.
4. Calculate the curvature of a smooth curve.
5. Find the domain of a function of several variables.
6. Find level curves of a function of 2 variables and sketch a contour map.
7. Find level surfaces of a function of 3 variables.
8. Calculate limits of a function of several variables.
9. Determine whether a function of several variables is continuous at a point.
10. Calculate partial derivatives of functions of several variables.
11. Determine the slope in the $x$ or $y$ directions of a surface in three dimensions.
12. Calculate mixed partial derivatives.
13. Find the total differential of a function of several variables.
14. Determine whether a function is differentiable at a given point.
15. Chain rule for functions of several variables.
16. Implicit partial differentiation.