Homework 03-solutions

Homework 03-solutions - Version 028 – Homework 03 –...

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: Version 028 – Homework 03 – Helleloid – (58250) 1 This print-out should have 23 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 these statements are true without further restrictions on f ? A. f is defined on ( a, 5) ∪ (5 , b ) for some a < 5 < b . B. As x approaches 5 , f ( x ) approaches 4 . C. Range of f contains 4 . 1. B and C only 2. A only 3. A and B only correct 4. None of them 5. C only 6. All of them 7. A and C only 8. B only Explanation: A. True: f ( x ) needs only be defined near x = 5. B. True: definition of limit C. Not True: f ( x ) needs only AP- PROACH 4. keywords: Stewart5e, True/False, definition limit limit 002 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 ) = 7 2. lim x → - 2 f ( x ) = 12 3. lim x → - 2 f ( x ) does not exist 4. lim x → - 2 f ( x ) = 8 5. lim x → - 2 f ( x ) = 4 correct 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. 003 10.0 points Below is the graph of a function f . Version 028 – Homework 03 – Helleloid – (58250) 2 2 4 − 2 − 4 2 4 − 2 − 4 Use the graph to determine lim x → 3 f ( x ). 1. lim x → 3 f ( x ) = 1 2. lim x → 3 f ( x ) = − 2 3. lim x → 3 f ( x ) = − 1 4. lim x → 3 f ( x ) = 0 5. lim x → 3 f ( x ) does not exist correct Explanation: From the graph it is clear that f has a left hand limit at x = 3 which is equal to − 2; and a right hand limit which is equal to 0. Since the two numbers do not coincide, the limit lim x → 3 f ( x ) does not exist . 004 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. 1. both L 1 and L 2 exist 2. L 1 exists, but L 2 doesn’t 3. L 1 doesn’t exist, but L 2 does correct 4. neither L 1 nor L 2 exists Explanation: For x > 0 the graph of f oscillates but the oscillations do not get smaller and smaller as x approaches 0; so L 1 does not exist. But for x < 0, the graph oscillates and the oscillations get smaller and smaller as x approaches 0; in fact, the oscillation goes to 0 as x approaches 0, so L 2 exists. Consequently, L 1 does not exist, but L 2 does . 005 10.0 points Consider the function f ( x ) = 2 − x, x < − 1 x, − 1 ≤ x < 3 ( x − 3) 2 , x ≥ 3 . Find all the values of a for which the limit lim x → a f ( x ) exists, expressing your answer in interval no- tation....
View Full Document

This note was uploaded on 12/04/2009 for the course M 408k taught by Professor Schultz during the Fall '08 term at University of Texas.

Page1 / 10

Homework 03-solutions - Version 028 – Homework 03 –...

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