HW03-solutions - white (taw933) HW03 ben-zvi (55600) 1 This...

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: white (taw933) HW03 ben-zvi (55600) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Suppose lim x 5 f ( x ) = 4 . Which of the following statements are true without further restrictions on f ? A. Range of f need not contain 4 . B. f is defined on ( a, 5) (5 , b ) for some a < 5 < b . C. As f ( x ) approaches 4 , x approaches 5 . 1. A only 2. None of them 3. All of them 4. B only 5. A and B only correct 6. A and C only 7. B and C only 8. C only Explanation: A. True: f ( x ) need only APPROACH 4. B. True: f ( x ) need only be defined NEAR x = 5. C. Not True: f ( x ) approaches 4 AS x ap- proaches 5. keywords: True/False, LimitDefn, limit 002 (part 1 of 2) 10.0 points 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. II only 2. Both I and II correct 3. Neither I nor II 4. I only Explanation: If f ( x ) is close to 0, then | f ( x ) | also must be close to 0. Conversely, if | f ( x ) | is close to 0, f ( x ) must also be close to 0. Therefore Both I and II are true . 003 (part 2 of 2) 10.0 points 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. II only 2. Neither I nor II 3. I only correct 4. Both I and II Explanation: If f ( x ) is close to L , then | f ( x ) | must be close to | L | no matter what the value of L is. So I is true. But II not true for all L and c . To see that, let f ( x ) = x , c = 2 and L = 2. Then lim x c | f ( x ) | = lim x - 2 | x | = 2 = | L | . white (taw933) HW03 ben-zvi (55600) 2 On the other hand, lim x c f ( x ) = lim x - 2 x = 2 negationslash = L . Consequently, Only I is true . 004 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. lim x - 2 f ( x ) = 4 correct 2. lim x - 2 f ( x ) = 7 3. lim x - 2 f ( x ) = 12 4. lim x - 2 f ( x ) does not exist 5. lim x - 2 f ( x ) = 8 Explanation: From the graph it is clear the f has both a left hand limit and a right hand limit at x = 2; in addition, these limits coincide. Thus lim x - 2 f ( x ) = 4 . 005 10.0 points If f oscillates faster and faster when x ap- proaches 0 as indicated by its graph determine which, if any, of L 1 : lim x 0+ f ( x ) , L 2 : lim x - f ( x ) exist....
View Full Document

Page1 / 9

HW03-solutions - white (taw933) HW03 ben-zvi (55600) 1 This...

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