Math Xb Spring 2004Midterm 2 Review Guide1 TopicsMidterm 1 will cover §21.1–21.4, §22.1-22.3, and App e ndices F and G in our textbook, Calculus: An In-tegrated Approach to Functions and Their Rates of Change. In particular, you will be responsible for thefollowing topics.Chapter 21: Differentiation of Trig Functions• To know the derivatives of the six trigonometric functions.• To find derivatives of more complex functions that involve trigonometric functions.• To solve related rates problems involving trig functions.• To solve optimization problems involving trig functions.• To solve curve-sketching problems involving trig functions.• To know how one can find the derivatives of the inverse trig functions using implicit differentiation.• To know the derivatives of sin−1, tan−1, and cos−1.Appendices F and G: L’Hˆopital’s Rule and Newton’s Method• To recognize the indeterminate forms00,∞∞, 0 · ∞, 1∞, ∞0, and 00.• To evaluate the indeterminate forms00,∞∞, 0 · ∞, 1∞, ∞0, and 00using L’Hˆopital’s Rule.• To understand how Newton’s Method works and how it can go wrong.• To approximate roots of functions iteratively using Newton’s Method.Chapter 22: Net Change, Area, and the Definite Integral• To understand the relationship between the definite integral and the questions1. Give n a rate function, how do we calculate the net change in amount?2. How do we calculate the signed area between the graph of a function and the horizontal axis?and to use these relationships to solve problems (such as §22.1 #1, §22.2 #5, and §22.3 #3)• To approximate a definite integral (or net change or signed area) using left- and right-hand sums.• To approximate the net change in amount given sample points on a rate function using left- andright-hand sums• To evaluate a definite integral (or net change or signed area) using geometric area formulas• To understand the definition of the definite integral2 Suggested ExercisesIn addition to working on the suggested exercises listed below, you are encouraged to review homeworkproblems, worksheets, and labs.Chapter 21• §21.2 #4, 5, 7, 9, 15• §21.3 #2, 6, 13, 15, 17 (a)• §21.4 #6, 8, 9Appendices F and G• App. F #1, 2, 5, 12, 13, 18• App. G #2, 4, 8Chapter 22• §22.1 #2, 8, 9• §22.2 #7, 8• §22.3 #2, 4,