This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Granillo, Yvette Final 1 Due: Dec 14 2005, 1:00 pm Inst: Edward Odell 1 This printout should have 25 questions. Multiplechoice 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...
View Full
Document
 Spring '08
 schultz

Click to edit the document details