HW03-solutions

# HW03-solutions - le(chl528 HW03 Gilbert(57195 This...

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

le (chl528) – HW03 – Gilbert – (57195) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Suppose that f ( x ) is defined for all x in U = (5 , 6) (6 , 7) and that lim x 6 f ( x ) = L. Which of the following statements are then true? A. if L > 0 , then f ( x ) > 0 on U ; B. if f ( x ) > 0 on U , then L 0; C. if L = 0 , then f ( x ) = 0 on U . 1. B , C only 2. B only correct 3. A , C only 4. each of A , B , C 5. A , B only 6. none of A , B , C Explanation: A. False: consider the function f ( x ) = 1 - 2 | x - 6 | . Its graph is 2 4 6 so lim x 6 f ( x ) = 1 . But on (5 , 11 2 ) and on ( 13 2 , 7) we see that f ( x ) < 0. B. True: if f ( x ) > 0 on U , then on U the graph of f always lies above the x -axis. So as x approaches 6, the point ( x, f ( x )) on the graph approaches the point (6 , L ). Thus L 0; notice that L = 0 can occur as the graph 2 4 6 2 of f ( x ) = | x - 6 | shows. C. False: consider the function f ( x ) = | x - 6 | . Its graph 2 4 6 2 shows that f ( x ) > 0 for all x = 6, but lim x 6 | x - 6 | = 0 . keywords: limit, definition of limit, properties of limits, T/F, True/False 002 (part 1 of 2) 10.0 points (i) Which of the following statements are true for all values of c ? I. lim x c f ( x ) = 0 = lim x c | f ( x ) | = 0 . II. lim x c | f ( x ) | = 0 = lim x c f ( x ) = 0 . 1. I only 2. II only 3. neither I nor II

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

View Full Document
le (chl528) – HW03 – Gilbert – (57195) 2 4. both I and II correct Explanation: 003 (part 2 of 2) 10.0 points (ii) Which of the following statements are true for all c and all L ? I. lim x c f ( x ) = L = lim x c | f ( x ) | = | L | . II. lim x c | f ( x ) | = | L | = lim x c f ( x ) = L. 1. I only correct 2. both I and II 3. neither I nor II 4. II only Explanation: 004 10.0 points A function f is defined piecewise for all x = 0 by f ( x ) = 3 + 1 2 x, x < - 2 , 5 2 x, 0 < | x | 2 , 5 + x - 1 2 x 2 , x > 2 . By first drawing the graph of f , determine all the values of a at which lim x a f ( x ) exists, expressing your answer in interval no- tation. 1. ( -∞ , - 2) ( - 2 , 0) (0 , ) 2. ( -∞ , - 2) ( - 2 , 0) (0 , 2) (2 , ) 3. ( -∞ , 0) (0 , ) 4. ( -∞ , 2) (2 , ) 5. ( -∞ , 0) (0 , 2) (2 , ) 6. ( -∞ , - 2) ( - 2 , ) correct 7. ( -∞ , - 2) ( - 2 , 2) (2 , ) Explanation: The graph of f is 2 4 - 2 - 4 2 4 - 2 - 4 and inspection shows that lim x a f ( x ) will exist only for a in ( -∞ , - 2) ( - 2 , ) .
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern