# hw 3 - silva(jrs4378 Hw 03 gualdani(56455 This print-out...

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silva (jrs4378) – Hw 03 – gualdani – (56455) 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 1+ x 2 x 1 . 1. limit = 2. limit = 2 3. limit = −∞ correct 4. none of the other answers 5. limit = 2 Explanation: For 1 < x < 2 we see that x 2 x 1 < 0 . On the other hand, lim x 1+ x 1 = 0 . Thus, by properties of limits, lim x 1+ x 2 x 1 = −∞ . 002 (part 2 of 3) 10.0 points (ii) Determine the value of lim x 1 - x 2 x 1 . 1. limit = correct 2. none of the other answers 3. limit = 2 4. limit = −∞ 5. limit = 2 Explanation: For x < 1 < 2 we see that x 2 x 1 > 0 . On the other hand, lim x 1 - x 1 = 0 . Thus, by properties of limits, lim x 1 - x 2 x 1 = . 003 (part 3 of 3) 10.0 points (iii) Determine the value of lim x 1 x 2 x 1 . 1. limit = −∞ 2. limit = 3. limit = 2 4. none of the other answers correct 5. limit = 2 Explanation: If lim x 1 x 2 x 1 exists, then lim x 1+ x 2 x 1 = lim x 1 - x 2 x 1 . But as parts (i) and (ii) show, lim x 1+ x 2 x 1 negationslash = lim x 1 - x 2 x 1 . Consequently, lim x 1 x 2 x 1 does not exist .

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silva (jrs4378) – Hw 03 – gualdani – (56455) 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 3 f ( x ). 1. lim x 3 f ( x ) = 2 2. lim x 3 f ( x ) = 1 3. lim x 3 f ( x ) does not exist correct 4. lim x 3 f ( x ) = 1 5. lim x 3 f ( x ) = 0 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 . 005 10.0 points Below is the graph of a function f . -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 2 4 6 2 4 6 2 4 6 8 2 4 Use the graph to determine lim x 3 - f ( x ) . 1. limit does not exist 2. limit = 5 correct 3. limit = 2 4. limit = 3 2 5. limit = 4 Explanation: As the graph shows, lim x 3 - f ( x ) = 5 . 006 10.0 points If f oscillates faster and faster when x ap- proaches 0 as indicated by its graph
silva (jrs4378) – Hw 03 – gualdani – (56455) 3 determine which, if any, of L 1 : lim x 0+ f ( x ) , L 2 : lim x 0 - f ( x ) exist. 1. both L 1 and L 2 exist 2. L 1 exists, but L 2 doesn’t 3. neither L 1 nor L 2 exists 4. L 1 doesn’t exist, but L 2 does correct 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 .

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