This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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....
View
Full
Document
 Spring '11
 Jensen

Click to edit the document details