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Unformatted text preview: 22M:031 — Practice Problems for Midterm Exam 2 MIDTERM EXAM 2 is Tuesday, November 13, 2007, 5:307:00 PM in MH Auditorium (in MacBride Hall). You sit the same way as for Exam 1 in MH Auditorium (see http://www.math.uiowa.edu/ ∼ fbleher/m31examseating.html). What to bring to the test: You are allowed to bring 1 single sheet (8.5 × 11 sq.in.) with handwritten notes of your choice. This must be original, and you must prepare it yourself. NO CALCULATORS, NO COMPUTERS, NO OTHER AIDS are allowed during Midterm 2. Do not bring any cell phones or other electronic devices to the exam room. Material covered by Exam 2: 3.7–3.10, 4.1–4.6, 4.8, 5.1–5.6, 6.1 (everything covered up to and including Friday, November 9). How to prepare for Exam 2: Go over the Lecture notes and do the Assignments. If you need more practice, do more oddnumbered problems. Do the practice problems. Doing the practice problems ALONE may not be enough to prepare for the test. Office hours and review session in exam week: Office hours: Monday, November 12, 2:003:30 PM in 225K MLH. Review Session: Monday, November 12, 2007, 6:307:30 PM in PBB, W10. Practice Problems for Midterm Exam 2. The practice problems show you how problems can be phrased on the test, but the actual problems on the test may use different functions and/or numbers. I. Logarithmic differentiation (Sec. 3.7). 1. Using logarithmic differentiation, find the derivative of y = s t t + 1 at t = 1. 2. Using logarithmic differentiation, find the slope of the tangent to the graph of y = x √ x 2 + 1 ( x + 1) 2 / 3 at x = 7. 3. Using logarithmic differentiation, find the derivative of y = (sin x ) x +1 at x = π/ 2. 4. Using logarithmic differentiation, find the derivative of y = (ln x ) ln x . II. Inverse trigonometric functions (Sec. 3.8). 1. Find the tangent line to the graph of y = ln (tan 1 ( x + 1)) at x = 0. 2. If r ( t ) = ( t 2 1) sin 1 ( √ 2 t ), find r (1 / 2). 3. Find the derivative of y = csc 1 ( e x ) + cot 1 ( x 1). III. Related rates (Sec. 3.9). 1. A 13ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft from the house, the base is moving at a rate of 5 ft/sec. Find the rate at which the top of the ladder is sliding down the wall then. 1 2. A person flies a kite at a height of 300 ft, the wind carrying the kite horizontally away from them at a rate of 25 ft/sec. How fast does the person have to let out the string when the kite is 500 ft away from them? 3. Two commercial airplanes are flying at 40,000 ft along straightline courses that intersect at right angles. Plane A is approaching the intersection at a speed of 442 knots (nautical miles per hour), plane B is approaching the intersection at a speed of 481 knots. Find the rate at which the distance between the planes is changing when A is 5 nautical miles from the intersection point, and B is 12 nautical miles away from the intersection points....
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 Spring '08
 Stroyan
 Math, Calculus, Inflection Points, Sec., nautical miles, logarithmic differentiation, MH Auditorium

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