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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 – find all choices before answering. 001(part1of3)10.0points 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: For 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(part2of3)10.0points 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: For 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(part3of3)10.0points 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 negationslash = lim x 2 - x 4 x 2 . Consequently, lim x 2 x 4 x 2 does not exist . 004(part1of2)10.0points
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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(part2of2)10.0points 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.
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