Example

Section	You should be able to …	Example	Review Exercises
12.1	1 Work with functions of two or three variables (p. 810)	1–3	1–9
	2 Graph functions of two variables (p. 812)	4	10–13
	3 Graph level curves (p. 812)	5, 6	14–16
	4 Describe level surfaces (p. 815)	7, 8	17, 18
12.2	1 Define the limit of a function of several variables (p. 819)
	2 Find a limit using properties of limits (p. 821)	1	19, 20
	3 Examine when limits exist (p. 822)	2–4	21, 22
	4 Determine whether a function is continuous (p. 824)	5–7	23–25
12.3	1 Find the partial derivatives of a function of two variables (p. 829)	1, 2	26–31, 41
	2 Interpret partial derivatives as the slope of a tangent line (p. 831)	3	32, 33
	3 Interpret partial derivatives as a rate of change (p. 832)	4–6	34(a), (b)
	4 Find second-order partial derivatives (p. 834)	7, 8	35, 36
	5 Find the partial derivatives of a function of \(n\) variables (p. 836)	9, 10	37–40
12.4	1 Find the change in \(z=f(x,y)\) (p. 841)	1	42
	2 Show that a function of two variables is differentiable (p. 841)	2, 3	43
	3 Use the differential \(dz\) to approximate a change in \(z\) (p. 844)	4–6	44, 45, 48–51
	4 Find the differential of a function of three or more variables (p. 846)	7	46, 47
12.5	1 Differentiate functions of two or more variables where each variable is a function of a single variable (p. 849)	1–3	34(c), 52, 53
	2 Differentiate functions of two or more variables where each variable is a function of two or more variables (p. 851)	4, 5	54, 55
	3 Differentiate an implicitly-defined function of two or more variables (p. 853)	6, 7	56, 57
	4 Use a Chain Rule in a proof (p. 855)	8	58