cal9 - choi (kc24547) HW09 BERG (56525) 1 This print-out...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: choi (kc24547) HW09 BERG (56525) 1 This print-out should have 22 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Determine if lim x 1 parenleftBig x 3 + 7 x 2 + x + 1 x 2 + 3 parenrightBig exists, and if it does, find its value. 1. limit = 5 4 2. limit does not exist 3. limit = 3 2 correct 4. limit = 6 5. limit = 5 Explanation: Both the limits for the numerator and de- nominator exist and the limit of the denom- inator is not equal zero. Thus LHospitals rule does not apply. Now lim x 1 ( x 3 + 7 x 2 + x + 1) = 6 , while lim x 1 ( x 2 + 3) = 4 . Consequently, by Properties of limits, limit = 3 2 . keywords: 002 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. A only 2. B only correct 3. none of them 4. A and B only 5. B and C only 6. C only 7. all of them 8. A and C only 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. 003 10.0 points choi (kc24547) HW09 BERG (56525) 2 Determine the value of lim x f ( x ) g ( x ) when f ( x ) = e 3 x- 1 , g ( x ) = x 2 + 5 x . 1. limit = 3 2 2. limit = 2 5 3. limit = 2 3 4. limit = 3 5 correct 5. limit = 5 2 6. limit does not exist Explanation: Since f, g are differentiable functions such that lim x f ( x ) = lim x g ( x ) = 0 , LHospitals Rule can be applied: lim x f ( x ) g ( x ) = lim x f ( x ) g ( x ) = lim x 3 e 3 x 2 x + 5 . Consequently, lim x f ( x ) g ( x ) = 3 5 . 004 10.0 points Find the value of lim x + 6 x- ln x 2 x . 1. limit = 2 2. limit = 6 3. limit = 0 4. limit = 3 5. none of the other answers 6. limit = correct 7. limit =- Explanation: Lets first check if the given limit is an indeterminate form. Now ln x is defined for x > 0 and the graph of ln x has a vertical asymptote at x = 0; in addition, lim x + ln x =- . On the other hand, 6 x- ln x 2 x = 3- ln x 2 x . Thus lim x + 6 x- ln x 2 x = 3 + , which is not an indeterminate form. In fact, since the second term is positive, we see that lim x + 6 x- ln x 2 x = . 005 10.0 points Determine if lim x sin 1 (2 x ) tan 1 (3 x ) exists, and if it does, find its value....
View Full Document

Page1 / 12

cal9 - choi (kc24547) HW09 BERG (56525) 1 This print-out...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online