Review for exam 1_pdf

# Review for exam 1_pdf - rabbani(tar547 – Review Exam 01...

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Unformatted text preview: rabbani (tar547) – Review Exam 01 – Fouli – (58395) 1 This print-out should have 31 questions. Multiple-choice 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 x-axis is given (in feet) by s ( t ) = 5 t 2 − 2 t + 5 . Determine the average velocity of the particle over the time interval [1 , 3]. 1. average vel. = 20 ft/sec 2. average vel. = 21 ft/sec 3. average vel. = 18 ft/sec correct 4. average vel. = 22 ft/sec 5. average vel. = 19 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) = 5 × 9 − 2 × 3 + 5 = 44 feet , while s (1) = 5 − 2 + 5 = 8 feet . Consequently, avg. vel. = 44 − 8 2 = 18 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 does not exist correct 2. limit = 9 3. limit = 14 4. limit = 8 5. limit = 6 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 . rabbani (tar547) – Review Exam 01 – Fouli – (58395) 2 2 4 − 2 − 4 2 4 − 2 − 4 Use the graph to determine lim x → 3 f ( x ). 1. limit = − 1 2. limit = − 2 correct 3. limit = 0 4. does not exist 5. limit = 1 Explanation: From the graph it is clear that the limit lim x → 3 − f ( x ) = − 2 , from the left and the limit lim x → 3+ f ( x ) = − 2 , from the right exist and coincide in value. Thus the two-sided lim x → 3 f ( x ) = − 2 . 004 10.0 points Determine lim x → x − 1 x 2 ( x + 9) . 1. limit = 1 2. limit = − 1 9 3. none of the other answers 4. limit = 0 5. limit = ∞ 6. limit = −∞ correct Explanation: Now lim x → x − 1 = − 1 . On the other hand, x 2 ( x + 9) > 0 for all small x , both positive and negative, while lim x → x 2 ( x + 9) = 0 . Consequently, limit = −∞ . keywords: evaluate limit, rational function 005 10.0 points Determine if lim x → x 7 + 6 x 5 3 x 6 + 5 x 8 exists, and if it does, find its value. 1. limit = 6 2. limit = 0 3. limit = −∞ 4. none of the other answers correct 5. limit = + ∞ Explanation: Since x 7 + 6 x 5 3 x 6 + 5 x 8 = x 2 + 6 x (3 + 5 x 2 ) , we see that none of 6 , + ∞ , , −∞ rabbani (tar547) – Review Exam 01 – Fouli – (58395) 3 can be the limit because x 2 + 6 x (3 + 5 x 2 ) −→ + ∞ as x → 0+, while x 2 + 6 x (3 + 5 x 2 ) −→ −∞ as x → − . Consequently, none of the other answers is the only true statement....
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Review for exam 1_pdf - rabbani(tar547 – Review Exam 01...

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