Exam3_2 9 - 1 2 correct Explanation Since f g are...

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Taylor, Douglas – Exam 3 – Due: Dec 5 2007, 1:00 am – Inst: JEGilbert 9 B. lim x 1 g ( x ) G ( x ) ; C. lim x 1 F ( x ) g ( x ) ; are indeterminate forms? 1. B and C only 2. A and C only 3. C only 4. A only 5. all of them 6. none of them 7. B only correct 8. A and B only Explanation: A. By properties of limits lim x 1 f ( x ) g ( x ) = 0 · 0 = 0 , so this limit is not an indeterminate form. B. Since lim x 1 = ∞· 0 , this limit is an indeterminate form. C. By properties of limits lim x 1 F ( x ) g ( x ) = 2 0 = 1 , so this limit is not an indeterminate form. keywords: 016 (part 1 of 1) 10 points Determine the value of lim x 0 f ( x ) g ( x ) when f ( x ) = e x - 1 , g ( x ) = x 6 + 2 x. 1. limit = 1 3 2. limit = 3 3. limit = 6 4. limit = 1 6 5. limit does not exist 6. limit =
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Unformatted text preview: 1 2 correct Explanation: Since f, g are diFerentiable functions such that lim x → f ( x ) = lim x → g ( x ) = 0 , L’Hospital’s Rule can be applied: lim x → f ( x ) g ( x ) = lim x → f ( x ) g ( x ) = lim x → e x 6 x 5 + 2 . Consequently, lim x → f ( x ) g ( x ) = 1 2 . keywords: limit, indeterminate form, L’Hospital, exp function, 017 (part 1 of 1) 10 points Determine if lim x →∞ (ln x ) 2 3 x + 6 ln x exists, and if it does, ±nd its value. 1. limit = 3 2. limit = 0 correct...
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This note was uploaded on 02/14/2012 for the course MATH 408 K taught by Professor Clark,c.w./hoy,r.r during the Spring '08 term at University of Texas.

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