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Unformatted text preview: jiwani (amj566) – Review Exam 01 – Fouli – (58395) 1 This printout should have 31 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points After t seconds the displacement, s ( t ), of a particle moving rightwards along the xaxis is given (in feet) by s ( t ) = 3 t 2 − 2 t + 6 . Determine the average velocity of the particle over the time interval [1 , 3]. 1. average vel. = 13 ft/sec 2. average vel. = 9 ft/sec 3. average vel. = 10 ft/sec correct 4. average vel. = 12 ft/sec 5. average vel. = 11 ft/sec Explanation: The average velocity over a time interval [ a, b ] is given by dist travelled time taken = s ( b ) − s ( a ) b − a . For the time interval [1 , 3], therefore, ave. vel. = s (3) − s (1) 3 − 1 ft/sec . Now s (3) = 3 × 9 − 2 × 3 + 6 = 27 feet , while s (1) = 3 − 2 + 6 = 7 feet . Consequently, avg. vel. = 27 − 7 2 = 10 ft/sec . 002 10.0 points Below is the graph of a function f . 2 4 6 − 2 − 4 − 6 2 4 6 8 − 2 − 4 Use the graph to determine lim x → 4 f ( x ) . 1. limit = 9 2. limit does not exist correct 3. limit = 8 4. limit = 5 5. limit = 7 Explanation: From the graph it is clear the f has a left hand limit at x = 4 which is equal to 9; and a right hand limit which is equal to − 2. Since the two numbers do not coincide, the limit does not exist . 003 10.0 points Below is the graph of a function f . jiwani (amj566) – Review Exam 01 – Fouli – (58395) 2 2 4 − 2 − 4 2 4 − 2 − 4 Use the graph to determine lim x → 4 f ( x ). 1. does not exist 2. limit = − 1 3. limit = − 2 4. limit = 0 5. limit = − 3 correct Explanation: From the graph it is clear that the limit lim x → 4 − f ( x ) = − 3 , from the left and the limit lim x → 4+ f ( x ) = − 3 , from the right exist and coincide in value. Thus the twosided lim x → 4 f ( x ) = − 3 . 004 10.0 points Determine lim x → x − 1 x 2 ( x + 3) . 1. limit = 0 2. limit = ∞ 3. limit = − 1 3 4. none of the other answers 5. limit = 1 6. limit = −∞ correct Explanation: Now lim x → x − 1 = − 1 . On the other hand, x 2 ( x + 3) > 0 for all small x , both positive and negative, while lim x → x 2 ( x + 3) = 0 . Consequently, limit = −∞ . keywords: evaluate limit, rational function 005 10.0 points Determine if lim x → x 5 + 6 x 3 4 x 8 + 6 x 10 exists, and if it does, find its value. 1. limit = −∞ 2. limit = + ∞ 3. limit = 6 4. limit = 0 5. none of the other answers correct Explanation: Since x 5 + 6 x 3 4 x 8 + 6 x 10 = x 2 + 6 x 5 (4 + 6 x 2 ) , we see that none of 6 , + ∞ , , −∞ jiwani (amj566) – Review Exam 01 – Fouli – (58395) 3 can be the limit because x 2 + 6 x 5 (4 + 6 x 2 ) −→ + ∞ as x → 0+, while x 2 + 6 x 5 (4 + 6 x 2 ) −→ −∞ as x → − . Consequently, none of the other answers is the only true statement....
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 Spring '11
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