This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Version 093 Exam 1 gualdani (56455) 1 This printout should have 20 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 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 2 f ( x ) . 1. limit = 2 2. limit = 9 3. limit does not exist correct 4. limit = 5 5. limit = 7 Explanation: From the graph it is clear the f has a left hand limit at x = 2 which is equal to 9; and a right hand limit which is equal to 6. Since the two numbers do not coincide, the limit does not exist . 002 10.0 points When f is the function defined by f ( x ) = braceleftbigg 3 x 7 , x < 1 , 5 x 8 , x 1 , determine if lim x 1 f ( x ) exists, and if it does, find its value. 1. limit = 5 2. limit = 6 3. limit = 2 4. limit = 4 correct 5. limit = 3 6. limit does not exist Explanation: The left hand limit lim x 1 f ( x ) depends only on the values of f for x > 2. Thus lim x 1 f ( x ) = lim x 1 3 x 7 . Consequently, limit = 3 1 7 = 4 . 003 10.0 points Determine lim x 8 x 8 x + 1 3 . 1. limit = 1 6 2. limit doesnt exist 3. limit = 6 correct 4. limit = 3 5. limit = 1 3 Version 093 Exam 1 gualdani (56455) 2 Explanation: After rationalizing the denominator we see that 1 x + 1 3 = x + 1 + 3 ( x + 1) 9 = x + 1 + 3 x 8 . Thus x 8 x + 1 3 = x + 1 + 3 for all x negationslash = 8. Consequently, limit = lim x 8 ( x + 1 + 3) = 6 . 004 10.0 points Determine lim h f (1 + h ) f (1) h when f ( x ) = 5 x 2 + 4 x + 1 . 1. limit does not exist 2. limit = 15 3. limit = 14 correct 4. limit = 18 5. limit = 17 6. limit = 16 Explanation: Since f (1 + h ) f (1) = 5(1 + h ) 2 + 4(1 + h ) + 1 10 = 14 h + 5 h 2 = h (14 + 5 h ) , we see that lim h f (1 + h ) f (1) h = lim h h (14 + 5 h ) h . Consequently, limit = 14 . 005 10.0 points Determine if the limit lim x sin 7 x 6 x exists, and if it does, find its value. 1. limit = 7 2. limit = 6 7 3. limit = 7 6 correct 4. limit = 6 5. limit doesnt exist Explanation: Using the known limit: lim x sin ax x = a , we see that lim x sin 7 x 6 x = 7 6 . 006 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 ) = 4 t 2 5 t + 7 ....
View Full
Document
 Spring '10
 Gualdani

Click to edit the document details