final_fa05

# final_fa05 - Name TA Name Math 20A Final Examination...

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Name: Section Number: TA Name: Section Time: Math 20A. Final Examination December 8, 2005 Turn of and put away your cell phone. No calculators or any other devices are allowed on this exam. You may use one page oF notes, but no books or other assistance on this exam. Read each question careFully, answer each question completely, and show all oF your work. Write your solutions clearly and legibly; no credit will be given For illegible solutions. IF any question is not clear, ask For clari±cation. 1. Let f ( x ) = r x + 2 x - 2 . (a) (2 points) Find the domain and range of f . (b) (4 points) Find f - 1 , the inverse of f . Be sure to state the domain and range of f - 1 . # Score 1 2 3 4 5 6 7 8 9 10 Σ

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2. (6 points) Find lim n →∞ 1 n 5 n X i =1 i 4 (Hint: Interpret the expression as a Riemann sum.)
3. (8 points) Let f ( x ) = x 3 - 6 x + 5 (a) Find the interval(s) where f is increasing and the intervals where f is decreasing. (b) Find the local maximum and local minimum value(s) of

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final_fa05 - Name TA Name Math 20A Final Examination...

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