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ExamFReview - MAC 1105 Some Final Review Questions Summer...

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MAC 1105: Some Final Review Questions, Summer 2010 Exam covers test 1 - 3 material, plus sections 4.3 - 5.6, 7.1 1. True or False: (a) 3 p x 3 + 27 = x + 3 (b) ln( 5 p e 2 ) = 5 2 (c) 1 2 is a solution to the equation log 25 1 5 = x . (d) The equation 1 x 1 y = 1 x y is true for all values of x and y . 2. Evaluate the following: a) 64 2 = 3 b) 4 p ( 3) 4 c) 2 0 + e ln 4 c) log 3 81 d) log 2 1 4 + log 4 4 3 3. Write in exponential form: log b 4 = x 4. Find each solution of the following equations: (a) x 3 + x 2 4 x = 4 (b) p 2 x + 3 = p x + 2 + 2 (c) 9 x +15 = 27 x (d) e x 2 = ( e x ) 2 1 e 3 5. Find each solution (real or complex) of the following: a) 2 x 2 + 2 x + 3 = 0 b) 3 x x 2 = 4 8 x c) 2 x 2 x 1 + 1 x = 1 2 x 1 6. Sketch the graph of the following. Find the domain and range of each. a) y = 2 x +1 b) f ( x ) = e x 2 c) g ( x ) = log 2 ( x 1) + 3 7. Find the inverse of f ( x ) = e x +3 . Sketch f and its inverse on the same graph. 8. Find the domain of the function f ( x ) = ln x 4 4 x 2 x + 3 . 9. Solve each equation: a) log 3 ( x 2 + x + 3) = 2 b) e 2 x +5 = 8 10. Write as the sum or di erence of logarithms: ln x p 2 x + 1 ( x 4) 4 11. Write as a single logarithm: a) 2 3 ln 8
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