final - Granillo, Yvette Final 1 Due: Dec 14 2005, 1:00 pm...

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Unformatted text preview: Granillo, Yvette Final 1 Due: Dec 14 2005, 1:00 pm Inst: Edward Odell 1 This print-out should have 25 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Below are the graphs of functions f and g . 4 8- 4 4 8- 4- 8 f : g : Use these graphs to determine lim x - 2 { f ( x ) + g ( x ) } . 1. limit = 3 2. limit = 0 3. limit does not exist correct 4. limit = 4 5. limit = 7 Explanation: From the graph it is clear that lim x - 2 { f ( x ) + g ( x ) } does not exist . keywords: Stewart5e, limit of a sum 002 (part 1 of 1) 10 points Determine lim x f ( x ) when f ( x ) = x- 1 x 2 ( x + 4) . 1. lim x f ( x ) = 0 2. lim x f ( x ) = 1 3. lim x f ( x ) = 4. lim x f ( x ) =- 1 4 5. lim x f ( x ) =- correct Explanation: Now lim x x- 1 =- 1 . On the other hand, x 2 ( x + 4) > 0 for all small x , both positive and negative, while lim x x 2 ( x + 4) = 0 . Thus lim x f ( x ) =- . keywords: Stewart5e, evaluating limit, nu- meric 003 (part 1 of 1) 10 points Determine lim x e 8 x- 8 x- 1 4 x 2 . 1. limit = 17 2 2. limit = 8 correct 3. limit doesnt exist Granillo, Yvette Final 1 Due: Dec 14 2005, 1:00 pm Inst: Edward Odell 2 4. limit = 15 2 5. limit = 9 Explanation: The limit in question is of the form: lim x f ( x ) g ( x ) where f and g are differentiable functions such that lim x f ( x ) = 0 , lim x g ( x ) = 0 . Thus LHospitals rule can be applied, so lim x f ( x ) g ( x ) = lim x f ( x ) g ( x ) . But lim x f ( x ) = 0 , lim x g ( x ) = 0 , in which case LHospitals rule has to be ap- plied again. Consequently, lim x f ( x ) g ( x ) = lim x f 00 ( x ) g 00 ( x ) . Since f 00 ( x ) = 64 e 8 x , g 00 ( x ) = 8 , it now follows that lim x e 8 x- 8 x- 1 4 x 2 = 8 . keywords: Stewart5e, 004 (part 1 of 1) 10 points Determine lim x 2 x tan- 1 (5 x ) . 1. limit = 2 2. limit does not exist 3. limit = 1 5 4. limit = 0 5. limit = 5 2 6. limit = 2 5 correct Explanation: Since the limit has the form lim x 2 x tan- 1 (5 x ) = , we use LHospitals Rule with f ( x ) = 2 x, g ( x ) = tan- 1 (5 x ) . For then lim x f ( x ) g ( x ) = lim x f ( x ) g ( x ) = lim x 2(1 + (5 x ) 2 ) 5 . Consequently, limit = 2 5 . keywords: Stewart5e, 005 (part 1 of 1) 10 points Find all values of x at which the function f defined by f ( x ) = x 2- 2 x- 15 x 2- 7 x + 10 , x 6 = 5, 8 3 , x = 5, is continuous, expressing your answer in in- terval notation. 1. (- ,- 2) (- 2 , ) Granillo, Yvette Final 1 Due: Dec 14 2005, 1:00 pm Inst: Edward Odell 3 2. (- ,- 2) (- 2 , 5) (5 , ) 3. (- , 2) (2 , 5) (5 , ) 4. (- , 2) (2 , ) correct 5. (- , 5) (5 , ) Explanation: After factorization f becomes f ( x ) = ( x- 5)( x + 3) ( x- 2)( x...
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final - Granillo, Yvette Final 1 Due: Dec 14 2005, 1:00 pm...

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