Review Exam One

# Review Exam One - MAC 2311 Exam 1 Review, Spring 2010 Exam...

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MAC 2311 Exam 1 Review, Spring 2010 Exam covers lectures 1 - 11 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 tan x sec x ± 1 d) lim x ! 2 + x 2 + 8 x ± 20 j 2 ± x j e) lim x ! 0 tan ± 1 ( x ± e x ) f) lim x ! 0 x 2 e sin( 1 x ) g) lim x !1 cos x x 2 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. Solve for x in [0 ; 2 ± ]: 2 sin 2 x ± sin(2 x ) = 0. 5. Solve for x : ln( x 2 ± 3) ± ln( x ± 1) = 0 6. Solve each inequality: a) j 2 x ± 1 j < 1 3 b) 2 cos x > 1 cos x for x in [0 ] 7. Evaluate cos ± cos ± 1 ² 4 5 ³ + tan ± 1 ² 1 2 ³´ . 8. Find the domains of the following functions: a) f ( x ) = x 2 x 2 ± 4 x b) g ( x ) = r x ± 9 x c) h ( x ) = x 3 ± 2 ln( x ) 9. If f ( x ) = 2 x and g ( x ) = 1 x 2 ± 4 , ±nd ( g

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## This note was uploaded on 02/10/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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Review Exam One - MAC 2311 Exam 1 Review, Spring 2010 Exam...

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