review1spring12 - M A C 2 3 1 1 Department of Mathematics...

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Unformatted text preview: M A C 2 3 1 1 Department of Mathematics MAC2311 EXAM 1 REVIEW PROBLEMS Instructor: Jane Smith Karly Jacobsen This review includes typical exam problems. It is not designed to be com- prehensive, but is a good representation of the topics covered on the exam. For problems with video solutions, follow this link. You may also pick up the Fall 2011 exam at Broward Teaching center. Try working it in 90 minutes. MAC2311 EXAM 1 REVIEW Part I: Multiple Choice 1. Identify the graph of f ( x ) = 1 + e 5- x . a. b. c. d. e. 2. A sample of bacteria doubles every 13 hours. Given that initially there are 400 bacteria, how many hours will it be until there are 2000 bacteria? a. 13 log 2 50 b. 50 log 2 13 c. 2 log 13 5 d. 2 log 5 13 e. 13 log 2 5 3. f ( x ) = tan x is an odd function. a. True b. False 2 MAC2311 EXAM 1 REVIEW 4. Given that f ( x ) = x- 2 3 x + 1 , find f- 1 ( x ). a. x + 2 1- 3 x b. x + 2 3 x- 1 c. x- 2 1- 3 x d. x + 3 1- 2 x e.- x- 3 1- 2 x 5. Evaluate lim x → 2- 4 x- x 3 | x- 2 | . a. 0 b.- 4 c.- 8 d. 4 e. 8 6. Find the inverse of the one-to-one function f ( x ) = x 1 + x . a. f- 1 ( x ) = 1 + x x b. f- 1 ( x ) = 1 x- 1 c. f- 1 ( x ) = 1- x x d. f- 1 ( x ) = x 1- x e. f- 1 ( x ) = 1 1 + x 7. Evaluate lim x → 2 f ( x ) if f ( x ) = 2 x- 1 x- 2 x 6 = 2 3 x = 2 . a.- 1 2 b. 3 c. 1 2 d.- 1 e. The limit does not exist. 3 MAC2311 EXAM 1 REVIEW 8. Let f ( x ) = 1 x 2- 1 and g ( x ) = √ x + 1. Find ( f ◦ g )( x ) and its domain. a. ( f ◦ g )( x ) = | x | √ x 2- 1 domain: (-∞ ,- 1) ∪ (1 , ∞ ) b. ( f ◦ g )( x ) = 1 x domain: (-∞ , 0) ∪ (0 , ∞ ) c. ( f ◦ g )( x ) = √ x + 1 x 2- 1 domain: (- 1 , 1) ∪ (1 , ∞ ) d. ( f ◦ g )( x ) = 1 x domain: [- 1 , 0) ∪ (0 , ∞ ) e. ( f ◦ g )( x ) = | x | √ x 2- 1 domain: (1 , ∞ ) 9. Find the value of k so that f ( x ) = { x 2- ln x + 2 k x ≤ e x 2- x x > e is continuous for all positive numbers.is continuous for all positive numbers....
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This note was uploaded on 02/14/2012 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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review1spring12 - M A C 2 3 1 1 Department of Mathematics...

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