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Unformatted text preview: vu (tv2894) – Homework 16 (Section 4.4) – miner – (55096) 1 This printout should have 4 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Determine if lim x →∞ x 3 5 x 2 x 3 + x 2 + 1 exists, and if it does, find its value. 1. limit = 3 2 2. limit = 0 3. limit = 1 2 correct 4. limit = 1 5. limit = 1 2 6. limit does not exist Explanation: After division by x 3 in both the numerator and denominator, we see that x 3 5 x 2 x 3 x 2 + 1 = 1 5 x 2 2 + 1 x + 1 x 3 . On the other hand, lim x →∞ parenleftBig 1 5 x 2 parenrightBig = 1 , while lim x →∞ parenleftBig 2 + 1 x + 1 x 3 parenrightBig = 2 . Consequently, lim x →∞ x 3 5 x 2 x 3 + x 2 + 1 exists and limit = 1 2 . 002 10.0 points A certain function f is known to have the properties lim x →−∞ f ( x ) = 6 , lim x →∞ f ( x ) = 4 ....
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 Fall '10
 Gualdini
 Calculus, Derivative, Limit, lim, Mathematical analysis, Limit of a function

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