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: Garcia, Ilse – Final 1 – Due: Dec 18 2007, 2:00 am – Inst: Fonken 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 At which point on the graph A B C D E F is the slope greatest ( i.e. , most positive)? 1. B 2. C correct 3. A 4. E 5. D 6. F Explanation: By inspection the point is C . keywords: slope, graph, change of slope 002 (part 1 of 1) 10 points Below is the graph of a function f . 2 4 2 4 2 4 2 4 Use the graph to determine lim x → 3 f ( x ). 1. does not exist 2. limit = 1 3. limit = 3 correct 4. limit = 0 5. limit = 2 Explanation: From the graph it is clear that the limit lim x → 3 f ( x ) = 3 , from the left and the limit lim x → 3+ f ( x ) = 3 , from the right exist and coincide in value. Thus the twosided lim x → 3 f ( x ) = 3 . keywords: limit, graph, limit at removable discontinuity 003 (part 1 of 1) 10 points Determine the limit lim x → 6 8 (6 x ) 2 . 1. none of the other answers Garcia, Ilse – Final 1 – Due: Dec 18 2007, 2:00 am – Inst: Fonken 2 2. limit = ∞ correct 3. limit = 4 3 4. limit = 4 3 5. limit =∞ Explanation: Since lim x → ( x 6) 2 = 0 and (6 x ) 2 > 0 for all x 6 = 0, we see that lim x → 6 8 (6 x ) 2 = ∞ . keywords: limit, rational function 004 (part 1 of 1) 10 points Determine if lim x →∞ x ‡ p x 2 + 4 x · exists, and if it does, find its value. 1. limit = 1 2. limit = 3 3. limit = 2 correct 4. limit = 5 2 5. limit does not exist 6. limit = 3 2 Explanation: After rationalization we see that x ‡ p x 2 + 4 x · = x µ x 2 + 4 x 2 √ x 2 + 4 + x ¶ = 4 x √ x 2 + 4 + x = 4 r 1 + 4 x 2 + 1 . On the other hand, lim x →∞ r 1 + 4 x 2 = 1 . Consequently, lim x →∞ x ‡ p x 2 + 4 x · exists and has limit = 2 . keywords: limit, limit at infinity, square root function, rationalize numerator 005 (part 1 of 1) 10 points Find the value of lim x → e 3 x e 3 x sin 2 x . 1. limit = 7 2 2. limit does not exist 3. limit = 3 2 4. limit = 3 correct 5. limit = 4 6. limit = 2 Explanation: Set f ( x ) = e 3 x e 3 x , g ( x ) = sin 2 x. Then f, g are everywhere differentiable func tions such that lim x → f ( x ) = lim x → g ( x ) = 0 . Thus L’Hospital’s Rule applies: lim x → f ( x ) g ( x ) = lim x → f ( x ) g ( x ) . Garcia, Ilse – Final 1 – Due: Dec 18 2007, 2:00 am – Inst: Fonken 3 Now f ( x ) = 3( e 3 x + e 3 x ) , g ( x ) = 2 cos 2 x, while lim x → f ( x ) = 6 , lim x → g ( x ) = 2 . Consequently, lim x → e 3 x e 3 x sin 2 x = 3 . keywords: 006 (part 1 of 1) 10 points Find all the values of x at which the func tion f defined by f ( x ) = x 4 2 x 2 4 x 16 is not continuous....
View
Full
Document
This note was uploaded on 02/22/2009 for the course M 58365 taught by Professor Gilbert during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Gilbert
 Calculus

Click to edit the document details