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m31practicefinal - 22M:031 Practice Problems for the Final...

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22M:031 — Practice Problems for the Final Exam The FINAL EXAM is on Thursday, December 20, 2007, 4:30-6:30 PM . Please make sure you go to the correct exam room, since some exam rooms will be very full. -→ ALL STUDENTS SHOULD SIT ON ODD-NUMBERED SEATS. -→ EXAM ROOMS WILL BE ACCORDING TO DISCUSSION SECTIONS: JONAS MEYER’s students will all be in the SEAMANS CENTER. JONAS MEYER, sec. 081 (meets at 8:30): 2217 SC JONAS MEYER, sec. 111 (meets at 11:30): 1505 SC ROWS 1-4 JONAS MEYER, sec. 123 (meets at 12:30): 2229 SC BOGDAN UDREA’s students will all be in the SEAMANS CENTER. BOGDAN UDREA, secs. 122 and 132: 1505 SC ROWS 5-10 FENG TIAN’s students will all be in VAN ALLEN HALL. FENG TIAN, secs. 082 and 112: LR2 VAN KIM HUERTER’s students will all be in the BIOLOGY BUILDING EAST. KIM HUERTER, secs. 121 and 131: 101 BBE What to bring to the test: You are allowed to bring 2 sheets (8.5 × 11 sq.in.) with handwritten notes of your choice. These must be original, and you must prepare them yourself. YOU MUST STAPLE THE 2 SHEETS TOGETHER. NO CALCULATORS, NO COMPUTERS, NO OTHER AIDS are allowed during the Final Exam. Do not bring any cell phones or other electronic devices to the exam room. Material covered by Final Exam: Sections 1.5, 1.6, 2.1, 2.2, 2.4–2.7, 3.1–3.10, 4.1–4.6, 4.8, 5.1–5.6, 6.1, 6.2, 8.1–8.5, 8.8 (everything covered up to and including Friday, December 14). The final exam is cumulative. How to prepare for the Final Exam: Take the practice problems as a guide of what types of problems may be on the final exam. If you do the practice problems and get stuck on some problems, you need to go back to the Lecture Notes and Assignments covering the corresponding topics. If you need more practice than given by the practice problems and the assignments, do more odd-numbered problems. Doing the practice problems ALONE may not be enough to prepare for the final exam. Office hours and review sessions: Last week of classes: Office hours: Monday, 12/10, and Wednesday, 12/12, 2:00–3:30 PM in 225K MLH. Review Session: Friday, December 14, during lecture. Final exam week: Review Session: Tuesday, December 18, 4:30–6:30 PM in LR1 VAN (Van Allen Hall). Practice Problems for the Final Exam. 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. 1
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Material before Midterm Exam 1: (Sections 1.5, 1.6, 2.1, 2.2, 2.4–2.7, 3.1–3.6) 1. Find the limit lim x →-∞ 4 x 6 - 11 x 5 + 13 x - 1 17 x 6 - x 5 + 21 x + 9 . 2. Find the limit lim x →- 1 2 x + 2 x 2 + 3 - 2 . 3. Find the limit lim x →- 4 + 7 - 3 x 2 8 + 2 x . 4. Define g (4) in a way that extends g ( x ) = x 2 - 16 x 2 - 3 x - 4 to be continuous at x = 4. 5. For what value of a is f ( x ) = x 2 - 1 , x < 3 2 ax, x 3 continuous at every x ? 6. Find the equation of the tangent line and the equation of the normal line to the curve y = 4 x 6 - 13 x 4 + 6 x 1 / 3 - 3 at the point (1 , - 6). 7. Find the derivative of f ( x ) = x 2 + 3 xe x 2 e x - 1 at x = 1.
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