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Final (v2) Fall 2010

# Final (v2) Fall 2010 - MATH 3 FINAL(Version 2 Instructor...

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MATH 3 FINAL (Version 2) 12/08/2010 Instructor: Nandini Bhattacharya Use of books, notes and graphing utilities is not permitted in this exam. Show all your work to get partial credit. Good luck! Your Name -------------------------------------------- Your TA -------------------------------------------- Max Your score Max Your score Problem 1: 15 Problem 11: 15 Problem 2: 15 Problem 12: 15 Problem 3: 25 Problem 13: 10 Problem 4: 10 Problem 14 (EC): 15 Problem 5: 25 Problem 6: 15 Problem 7: 20 Problem 8: 10 Problem 9: 15 Problem 10: 10 TOTAL:

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1. (15 points) Consider the function y = 2cos(2 x + π ) + 1 . Find the following: (a) (1 point) The amplitude of f. (b) (2 points) The period of f. (c) (2 points) The phase shift of f. (d) (6 points) The graph of f labeling all points. e) (4 points) Now graph y = 2sec(2 x + π ) + 1 into the same coordinate system above.
2. (15 points) Let f(x) = x + 3, and g(x) = x 2 + 4 x 1 . a) Find the minimum value of g f . b) Find the minimum value of f g . c) Are the results in parts (a) and (b) the same?

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3. (25 points) Find all solutions for the following functions: a) 3 3 x + 2 = 5 b) ln x = ln(2 x 1) ln x 2 ( ) c) 2sin θ + 3 = 0, all θ
d) 2cos 2 θ + sin 2 θ = 0 e) 4 cos 2 2 x 4 cos2 x + 1 = 0 0 x 2 π

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4. (10 points)
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