review1f11 - MAC 2311 Exam 1 Review, Fall 2011 Exam covers...

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MAC 2311 Exam 1 Review, Fall 2011 Exam covers lectures 1 - 10 This review is not necessarily inclusive of all topics covered in lecture and on the exam. It is meant to remind you of some key topics, and give you practice in putting concepts together. You should also review your lecture notes, homework assignments, and practice exam problems as well. Be sure you can work problems completely, without outside help, by the time of the exam. 1. Find the value of the limits: a) lim x ! 2 p x 2 + 6 x ± 4 x ± 2 b) lim x ! 2 1 2 ± 1 x 2 ± 2 2 ± x c) lim x ! 0 ± ln( x + 1) + e x ± 1 x 2 + 1 ² d) lim x ! 2 + x 2 + 8 x ± 20 j 2 ± x j e) lim x ! 0 sin ± 1 ( x ± e x 2 ) f) lim x ! 0 sin 1 x g) lim x ! 0 x 2 e sin(1 =x ) h) lim x ! 0 ± e 2 x i) lim x !±1 e 2 x 2. If f ( x ) = x 3 + 3 x 2 + 2 x x ± x 3 , ±nd a) lim x ! 0 + f ( x ) b) lim x 1 + f ( x ), c) lim x ! 1 ± f ( x ) and d) lim x !±1 f ( x ) . List all discontinuities and describe as in±nite, jump, or removable. Find each vertical and horizontal asymptote of f ( x ). 3. Sketch the following graphs: a) y = 2 cos( x ± ± 2 ) b) y = ( x + 1) j x ± 1 j c) If f ( x ) = p x , graph g ( x ) = 2 ± f ( x ± 3). 4. Let f ( x ) = (2 x + 1) 1 = 3 ± ( x 2 + 1)(2 x + 1) ± 2 = 3 2 x + 1 . Simplify the function and solve the equation f ( x ) = 0. 5. Solve for x in [0 ; 2 ± ]: cos 2 x + 5 cos x = 2 6. Solve for x : ln( x 2 ± 3) ± ln( x ± 1) = 0 b) log 4 ( x + 2) = log 2 x 7. Solve each inequality: a) ³ ³ ³ 1
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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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review1f11 - MAC 2311 Exam 1 Review, Fall 2011 Exam covers...

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