HW3 Calc - garcia (jjg2564) Hw 03 gualdani (56410) 1 This...

Info iconThis preview shows pages 1–4. 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

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: garcia (jjg2564) Hw 03 gualdani (56410) 1 This print-out should have 24 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 3) 10.0 points (i) Determine the value of lim x 4+ x 8 x 4 . 1. limit = 2 2. limit = 3. none of the other answers 4. limit = correct 5. limit = 2 Explanation: For 4 < x < 8 we see that x 8 x 4 < . On the other hand, lim x 4+ x 4 = 0 . Thus, by properties of limits, lim x 4+ x 8 x 4 = . 002 (part 2 of 3) 10.0 points (ii) Determine the value of lim x 4- x 8 x 4 . 1. limit = 2 2. limit = 3. none of the other answers 4. limit = correct 5. limit = 2 Explanation: For x < 4 < 8 we see that x 8 x 4 > . On the other hand, lim x 4- x 4 = 0 . Thus, by properties of limits, lim x 4- x 8 x 4 = . 003 (part 3 of 3) 10.0 points (iii) Determine the value of lim x 4 x 8 x 4 . 1. limit = 2. limit = 3. none of the other answers correct 4. limit = 2 5. limit = 2 Explanation: If lim x 4 x 8 x 4 exists, then lim x 4+ x 8 x 4 = lim x 4- x 8 x 4 . But as parts (i) and (ii) show, lim x 4+ x 8 x 4 negationslash = lim x 4- x 8 x 4 . Consequently, lim x 4 x 8 x 4 does not exist . garcia (jjg2564) Hw 03 gualdani (56410) 2 004 10.0 points Below is the graph of a function f . 2 4 2 4 2 4 2 4 Use the graph to determine lim x 2 f ( x ). 1. lim x 2 f ( x ) does not exist correct 2. lim x 2 f ( x ) = 4 3. lim x 2 f ( x ) = 3 4. lim x 2 f ( x ) = 5 5. lim x 2 f ( x ) = 2 Explanation: From the graph it is clear that f has a left hand limit at x = 2 which is equal to 5; and a right hand limit which is equal to 3. Since the two numbers do not coincide, the limit lim x 2 f ( x ) does not exist . 005 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. limit = 6 correct 2. limit = 4 3. limit = 2 4. limit = 2 5. limit does not exist Explanation: As the graph shows, lim x 2- f ( x ) = 6 . 006 10.0 points If f oscillates faster and faster when x ap- proaches 0 as indicated by its graph garcia (jjg2564) Hw 03 gualdani (56410) 3 determine which, if any, of L 1 : lim x 0+ f ( x ) , L 2 : lim x - f ( x ) exist. 1. L 1 exists, but L 2 doesnt correct 2. both L 1 and L 2 exist 3. L 1 doesnt exist, but L 2 does 4. neither L 1 nor L 2 exists Explanation: For x > 0 the graph of f oscillates but the oscillations get smaller and smaller as x approaches 0; in fact, the oscillation goes to 0 as x approaches 0, so L 1 exists. But for x < 0, the graph oscillates but the oscillations do not get smaller and smaller, so L 2 does not exist....
View Full Document

This note was uploaded on 10/08/2010 for the course MATH 408K taught by Professor Gualdani during the Fall '09 term at University of Texas at Austin.

Page1 / 11

HW3 Calc - garcia (jjg2564) Hw 03 gualdani (56410) 1 This...

This preview shows document pages 1 - 4. Sign up to view the full document.

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