review1f10

# review1f10 - MAC 2311 Exam 1 Review Fall 2010 Exam covers...

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MAC 2311 Exam 1 Review, Fall 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 1 ± sec x sin 2 x 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 ) = j x j , 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 1 ± x 2 j > 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) g ( x ) = r x ± 9 x b) h ( x ) = x 3 ± 2 ln( x ) 9. If f ( x ) = 1 ± x 2 and g ( x ) = 1 p 2 + x , ±nd ( f ² g )( x ) and its domain. Do the

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## This note was uploaded on 07/15/2011 for the course MATH 2311 taught by Professor T during the Spring '11 term at University of Florida.

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review1f10 - MAC 2311 Exam 1 Review Fall 2010 Exam covers...

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