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4 - Nguyen(ln4328 HW#4 treisman(54540 This print-out should...

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Nguyen (ln4328) – HW #4 – treisman – (54540) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find the value of lim x 1 10 x 3 5 x 2 if the limit exists. 1. limit = 2 3 correct 2. limit = 2 3 3. limit = 3 2 4. limit does not exist 5. limit = 3 2 Explanation: By rationalization 10 x 3 = (10 x ) 9 10 x + 3 = parenleftbigg x 1 10 x + 3 parenrightbigg , while 5 x 2 = (5 x ) 4 5 x + 2 = parenleftbigg x 1 5 x + 2 parenrightbigg . Thus 10 x 3 5 x 2 = 5 x + 2 10 x + 3 when x negationslash = 1. But lim x 1 5 x = 2 , lim x 1 10 x = 3 . Consequently, by the properties of limits, lim x 1 10 x 3 5 x 2 = 2 3 . 002 10.0 points Determine lim x 2 f ( x ) f (2) x 2 when f ( x ) = 5 x 2 2 x + 4 . 1. limit = 21 2. limit = 17 3. limit does not exist 4. limit = 19 5. limit = 18 correct 6. limit = 20 Explanation: Since f ( x ) f (2) = parenleftBig 5 x 2 2 x + 4 parenrightBig 20 = 5 x 2 2 x 16 = (5 x + 8)( x 2) , we see that f ( x ) f (2) x 2 = 5 x + 8 , for x negationslash = 2. Consequently, lim x 2 f ( x ) f (2) x 2 = 18 . Alternatively, if we recognize that lim x 2 f ( x ) f (2) x 2 = f (2) = (10 x 2) | x =2 , we see again that lim x 2 f ( x ) f (2) x 2 = 18 .
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Nguyen (ln4328) – HW #4 – treisman – (54540) 2 003 10.0 points Find the value of b , b 0, for which lim x 0 braceleftBig 4 x + b 1 x bracerightBig exists. 1. b = 2 2. b = 1 correct 3. b = 3 4. b = 4 5. b = 0 Explanation: We are told that lim x 0 braceleftBig 4 x + b 1 x bracerightBig = A for some value A , but we aren’t told what the particular value of A is. The question requires us to see exactly what value b must take for A to exist.
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