Math3A-Winter09-Practice

Math3A-Winter09-Practice - f ( x ) = -x if x <...

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Math 3A Exam 1 (Winter 2009)-Practice Name: Lecture Time: TA’s Name: Discussion Time: DIRECTIONS: Please do not open your exam until you are instructed to do so. Write your name and fill in the blanks corresponding to your lecture time, TA’s name, and discussion time. Show all your work. Answers without explanation will not receive credit. Scratch paper has been provided for your convenience, however it will not be graded. Calculators, notes and formula sheets are not allowed. There are six problems on the exam and each is worth 5 points. Problem Score Problem Score 1 /5 4 /5 2 /5 5 /5 3 /5 6 /5 Total /30 1
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1. Evaluate lim x 3 x 2 - 9 x 2 + 2 x - 3 3
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2. Let
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Unformatted text preview: f ( x ) = -x if x < 3-x if 0 x < 3 ( x-3) 2 if x > 3 Evaluate each limit, if it exists. (a) lim x + f ( x ) (b) lim x -f ( x ) (c) lim x 3 + f ( x ) (d) lim x 3-f ( x ) (e) Where is f discontinuous? 5 Scratch 6 3. Find the limit. (a) lim x -3 1 ( x + 3) 4 (b) lim x 3 x 2-1 2 x 2 + 7 7 Scratch 8 4. Prove that lim x x 2 cos(1 /x 2 ) = 0 9 Scratch 10 5. Find an interval of length 1 that contains a solution to x 4 + x-3 = 0 11 Scratch 12 6. Using the precise denition of a limit, prove that lim x 2 (14-5 x ) = 4 13...
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Math3A-Winter09-Practice - f ( x ) = -x if x <...

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