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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 doesn’t 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 L’Hospital’s 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 L’Hospital’s 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 L’Hospital’s 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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This test prep was uploaded on 04/16/2008 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas.
 Spring '08
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