exam1 - ) on [0 , 8] is graphed as follows. 1 2 3 4 5 6-1 y...

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MATH 3A – Winter 2008 Midterm I Jan 28, 2008 Name: Perm #: Schedule of discussion class: Instructions: The exam consists of 7 problems. You have 50 minutes to answer all questions. Please write full solutions, not just answers. Answers without jus- tifcation will get little or no partial credit. Show your work, explain your reasoning . You are not al- lowed to use any calculators, books or notes. Good luck. Problem Max Score 1 10 2 10 3 10 4 8 5 2 6 10 7 10 Total 60 1
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1. (10 point)Find all horizontal and vertical asymptotes of the function y = (3 x - 5)(2 x +3) (2 x - 4)( x +2) . 2. (10 point)Given g ( x ) = 3 x +5 2 x +7 , ±nd the formula for the inverse function of g ( x ). 2
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3. (10 point) Let f ( x ) = x if x < 0; x 2 if 0 x 2; 8 - x if 2 < x. (a) Graph the function f ( x ). (b) Evaluate lim x 2 + f ( x ) and lim x 2 - f ( x ). 3
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4. (8 point)The functions f ( x
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Unformatted text preview: ) on [0 , 8] is graphed as follows. 1 2 3 4 5 6-1 y 1 2 7 x 8 (a) Determine the values of a for which lim x a f ( x ) doesnt exist. (b) what is lim x 4+ f ( x )? (c) what is lim x 3-f ( x )? (d) What is f (3)? 5. (2 points)List all graphs which is described by an one-to-one function. A B C D E (a) a A,C, D (b) a B (c) a A,C (d) a E (e) a All of them (f) a None of them 4 6. (10 point)Evaluate the limit if it exists. (a) lim x 1-x 2-1 | x-1 | (b) lim x 2 x 3 + 8 x + 2 7. (10 points)Suppose f ( x ) and g ( x ) are continuous functions, lim x 7 [ f ( x ) + g ( x )] =-6, and lim x 7 [ f ( x )-g ( x )] = 11. What is f (7) g (7) ? 5...
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This note was uploaded on 04/07/2008 for the course MATH 3a taught by Professor Shu during the Winter '08 term at UCSB.

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exam1 - ) on [0 , 8] is graphed as follows. 1 2 3 4 5 6-1 y...

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