Problems for 221, fall 2001

The 221 Syllabus
 Section Subject Problems 1.2 Coordinates 1,13,15,16 1.3, 1.4 Increments, Slope of a line 1.5 Equation of Straight lines 10,11,15,19 1.7 Slope of a curve 1,2,12,13 1.8 Derivative of a function 1,2,3,6,8,12, 14, 22 1.9 Velocities and rates 1 (see Pblm12, § 1.8), 2, 8, 19, 20 1.10 Limits 1,2,4,6,7,9,12,15,16,17,18 2.2 Derivatives of polynomials 1,3,10,11,13,25,27 2.3 Product and Quotient rules 2,3,6,7,8,9,14 2.4 Inverse functions 1,2,3 2.5 Implicit Functions 1,2,3,7,19 2.8 Chain rule 6, 7, 9 2.9 Trigonometry review 2.10 Derivatives of sin, cos and tan 1,2,3,4,7,23,24,26,29,35,39 2.6 Increments (we skip differentials) 6,7,10 3.2 Related rates 1,2,3,7,8,9 3.3-3.4 Convexity and Concavity 1,2,3,5,7,8 3.5-3.6 Maxima and Minima 1,2,3,4,5,6,7 3.7-3.8 Rolle's and Mean Value Theorems (3.7) 4, (3.8) 1,7 3.9 l'Hôpitals's rule 1,3,6,7,8,9 3.10 Taylor's formula A hand out with problems will be provided 4.2 Indefinite integral and differential equations 1,2,3,6,9,10,14—24 4.3 Interpretations of the indefinite integral 1,3,4,6(!), 7,8,13,14 4.4 Integrals of trigonometric functions 1—10,25 4.5 Area under a curve 1,2,4,6,9 4.6 Area as a limit — 4.7 Area and calculus 1—4,9,10,12—15 4.8 The Fundamental Theorem of Calculus 6—14 (Sketch the region whose area is represented by each of these integrals) 18,20,22,23 4.9 Approximating integrals 5.2 Plane areas 1(b),2,3,4,6,8,9,10,11 5.3 Distance traveled 1,3,4,10,11,14 5.4 Volumes (in general) 1,2,3,5,9,10,11(a&b!),13(!),17 5.5 Volumes by shells &washers 1,3,6,8,10,12 6.1 Trig functions again 37 (no computations required!) 34, 38, (related rates review) 40, 45,46,47,48 49 50,51,52 6.2 The inverse trig functions 1,2,3,8(abcd)(no calculator) 6,9 On your graphing calculator look at the graph of y=sin-1(sinx). Explain. 6.3 Derivatives of inverse trig functions. 5,6,8,9(!),11, 16,17,18,20 6.4,6.5, 6.6, 6.7,6.8 Natural Logarithm, the exponential function and exponential growth. We deviate significantly from the textbook.Notes will be handed out.