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Homework 21

Homework 21 - vu(tv2894 Homework 21(Section 7.4 miner(55096...

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vu (tv2894) – Homework 21 (Section 7.4) – miner – (55096) 1 This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Determine f ( e ) when f ( x ) = x 2 (6 + (ln x ) 3 ) . 1. f ( e ) = 15 e 2. f ( e ) = 16 e 3. f ( e ) = 13 e 4. f ( e ) = 14 e 5. f ( e ) = 17 e correct Explanation: Using the Product and Power rules we see that f ( x ) = 2 x (6 + (ln x ) 3 ) + 3 x 2 (ln x ) 2 x = x (12 + 2(ln x ) 3 + 3(ln x ) 2 ) . At x = e , therefore, f ( e ) = 17 e . 002 10.0 points Use calculus to determine which one of the following could be the graph of f when f ( x ) = x - 2 ln parenleftBig x - 2 2 parenrightBig - 6 . 1. 2. correct 3. 4. 5.

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vu (tv2894) – Homework 21 (Section 7.4) – miner – (55096) 2 6. Explanation: Since the graph of y = ln x has a vertical asymptote at x = 0 and ln x is defined only for x > 0, the graph of f will have a vertical asymptote at x = 2 and will lie to the right of this asymptote. All the given graphs have these properties. We need, therefore, to look at f and f ′′ .
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