review1s11

# Review1s11 - MAC 2311 Exam 1 Review Spring 2011 Exam covers lectures 1 10 1 Find the value of the limits a lim x 2 p x 2 6 x Â 4 x Â 2 b lim x 2 1

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MAC 2311 Exam 1 Review, Spring 2011 Exam covers lectures 1 - 10 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 , ﬂnd 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 inﬂnite, 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 ]: cos2 x + 5cos x = 2 6. Solve for x : log 4 ( x 2 ¡ 3) ¡ log 4 ( x ¡ 1) = 0 7. Solve each inequality: a) j 1 ¡ x 2 j > 3 b) 2 cos x > 1 cos x for x in [0 ;… ] 8. Evaluate cos cos ¡ 1 ± 4 5 + tan ¡ 1 ± 1 2 ¶‚ .

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## This note was uploaded on 05/17/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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Review1s11 - MAC 2311 Exam 1 Review Spring 2011 Exam covers lectures 1 10 1 Find the value of the limits a lim x 2 p x 2 6 x Â 4 x Â 2 b lim x 2 1

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