HW4-solutions - wei (jw35975) HW4 milburn (54685) This...

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wei (jw35975) – HW4 – milburn – (54685) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 (part 1 of 3) 10.0 points Determine the value oF lim x 2+ x 4 x 2 . 1. none oF the other answers 2. limit = 2 3. limit = 4. limit = 2 5. limit = −∞ correct Explanation: ±or 2 < x < 4 we see that x 4 x 2 < 0 . On the other hand, lim x 2+ x 2 = 0 . Thus, by properties oF limits, lim x 2+ x 4 x 2 = −∞ . 002 (part 2 of 3) 10.0 points Determine the value oF lim x 2 - x 4 x 2 . 1. limit = 2 2. limit = −∞ 3. none oF the other answers 4. limit = correct 5. limit = 2 Explanation: ±or x < 2 < 4 we see that x 4 x 2 > 0 . On the other hand, lim x 2 - x 2 = 0 . Thus, by properties oF limits, lim x 2 - x 4 x 2 = . 003 (part 3 of 3) 10.0 points Determine the value oF lim x 2 x 4 x 2 . 1. none oF the other answers correct 2. limit = 2 3. limit = 2 4. limit = 5. limit = −∞ Explanation: IF lim x 2 x 4 x 2 exists, then lim x 2+ x 4 x 2 = lim x 2 - x 4 x 2 . But as parts (i) and (ii) show, lim x 2+ x 4 x 2 n = lim x 2 - x 4 x 2 . Consequently, lim x 2 x 4 x 2 does not exist . 004 (part 1 of 2) 10.0 points
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wei (jw35975) – HW4 – milburn – (54685) 2 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. Neither I nor II 2. Both I and II correct 3. II only 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 . 005 (part 2 of 2) 10.0 points Which of the following statements are true for all c and all L ? I. lim
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This note was uploaded on 10/25/2011 for the course MATHEMATIC 408K taught by Professor Milburn during the Fall '11 term at University of Texas at Austin.

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HW4-solutions - wei (jw35975) HW4 milburn (54685) This...

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