Limits (continued)-solutions HW 4

Limits (continued)-solutions HW 4 - handa (nh5757) Limits...

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handa (nh5757) – Limits (continued) – bormashenko – (54880) 1 This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points Determine which one oF the Following is the graph oF f ( x )= 2 x x - 2 . 1. correct 2. 3. 4. 5. 6. Explanation: The graph oF f will have a vertical asymp- tote at x - 2=0 , i.e. ,toth er igh to Fth e y -axis. This eliminates two oF the possible graphs. In addition, the graph oF f must pass through the origin, eliminating a third graph. To decide which oF the remaining three graphs is that oF f we look at the behaviour oF f near the asymptote: lim x 2 - f ( x -∞ , while lim x 2+ f ( x )=+ .
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handa (nh5757) – Limits (continued) – bormashenko – (54880) 2 Consequently, the graph of f must be keywords: limit, inFnity 002 10.0 points Determine lim x 0 x - 1 x 2 ( x +7) . 1. limit = - 1 7 2. none of the other answers 3. limit = 0 4. limit = -∞ correct 5. limit = 1 6. limit = Explanation: Now lim x 0 x - 1= - 1 . On the other hand, x 2 ( x > 0forallsmall x ,bothpos itiveandnegative ,wh ile lim x 0 x 2 ( x +7) = 0 . Consequently, limit = -∞ . keywords: evaluate limit, rational function 003 10.0 points Determine the limit lim x 3 8 ( x - 3) 2 . 1. limit = correct 2. limit = - 8 3 3. none of the other answers 4. limit = -∞ 5. limit = 8 3 Explanation: Since ( x - 3) 2 0fora l l x ,weseethat lim x 3 8 ( x - 3) 2 = . keywords: limit, rational function 004 10.0 points Determine lim x 0 csc x 5 x . 1. limit = correct 2. limit = - 1 5 3. limit = 1 5 4. limit = -∞ 5. none of the other answers Explanation:
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handa (nh5757) – Limits (continued) – bormashenko – (54880) 3 Since csc x 5 x = 1 5 x sin x > 0 for all small x ,bo thpo
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Limits (continued)-solutions HW 4 - handa (nh5757) Limits...

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