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Unformatted text preview: Version 160/ACCAA DGQ02 gilbert (55485) 1 This printout should have 3 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 1 2 3 4 5 6 7 AA AB AC AD BA BB BC 8 9 10 BACK NEXT BD CA CB CC CD 001 10.0 points Determine if lim x sin 1 (5 x ) tan 1 (4 x ) exists, and if it does, find its value. 1. limit = 4 5 2. limit does not exist 3. limit = 4 4. limit = 0 5. limit = 5 4 correct 6. limit = 5 Explanation: Since the limit has the form 0 / 0, it is in determinate and LHospitals Rule can be ap plied: lim x f ( x ) g ( x ) = lim x f ( x ) g ( x ) with f ( x ) = sin 1 (5 x ) , g ( x ) = tan 1 (4 x ) , and f ( x ) = 5 1 25 x 2 , g ( x ) = 4 1 + 16 x 2 . In this case, f ( x ) g ( x ) = 5 4 parenleftBig 1 + 16 x 2 1 25 x 2 parenrightBig 5 4 as x 0. Consequently, the limit exists and limit = 5 4 ....
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 Spring '07
 TextbookAnswers
 Calculus, lim, Mathematical analysis, Limit of a function, 0 g

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