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: saliyev (is4663) Quest Assignment 1 rodin (54520) 1 This printout should have 10 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points When f, g, F and G are functions such that lim x 1 f ( x ) = 0 , lim x 1 g ( x ) = 0 , lim x 1 F ( x ) = 2 , lim x 1 G ( x ) = , which, if any, of A. lim x 1 F ( x ) g ( x ) , B. lim x 1 g ( x ) G ( x ) , C. lim x 1 f ( x ) g ( x ) , are indeterminate forms? 1. B and C only 2. B only correct 3. A and C only 4. A and B only 5. C only 6. none of them 7. A only 8. all of them Explanation: A. By properties of limits lim x 1 F ( x ) g ( x ) = 2 = 1 , so this limit is not an indeterminate form. B. Since lim x 1 = , this limit is an indeterminate form. C. By properties of limits lim x 1 f ( x ) g ( x ) = 0 0 = 0 , so this limit is not an indeterminate form. 002 10.0 points Determine if lim x x 2 ln parenleftBig x + 3 x parenrightBig exists, and if it does, find its value. 1. limit = 3 2 correct 2. limit = 2 3 3. limit = 2 3 4. limit does not exist 5. limit = 0 6. limit = 3 2 Explanation: Since the limit has the form 0, it is indeterminate and LHospitals Rule can be applied: lim x f ( x ) g ( x ) = lim x f ( x ) g ( x ) with f ( x ) = ln parenleftBig x + 3 x parenrightBig , g ( x ) = 2 x , and f ( x ) = 1 x + 3 1 x , g ( x ) = 2 x 2 . saliyev (is4663) Quest Assignment 1 rodin (54520) 2 In this case, f ( x ) g ( x ) = x 2 2 parenleftBig x ( x + 3) x ( x + 3) parenrightBig = 3 2 parenleftBig x x + 3 parenrightBig 3 2 as x . Consequently, the limit exists and limit = 3 2 . 003 10.0 points Find the value of lim x 1 cos 2 x 5 sin 2 3 x . 1. limit does not exist 2. limit = 1 15 3. limit = 1 18 4. limit = 2 45 correct 5. limit = 7 90 Explanation: Set f ( x ) = 1 cos 2 x, g ( x ) = 5 sin 2 3 x . Then f, g are differentiable functions such that lim x f ( x ) = lim x g ( x ) = 0 ....
View Full
Document
 Spring '11
 RUSIN

Click to edit the document details