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Unformatted text preview: lawrence (cdl678) – Homework 1 – Odell – (56280) 1 This printout should have 32 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Determine if lim x →− 1 parenleftBig 5 x 2 + 1 x 2 + 1 parenrightBig exists, and if it does, find its value. 1. limit does not exist 2. limit = 3 correct 3. limit = 1 4. limit = 6 5. limit = 5 Explanation: Set f ( x ) = 5 x 2 + 1 , g ( x ) = x 2 + 1 . Then lim x →− 1 f ( x ) = 6 , lim x →− 1 g ( x ) = 2 . Thus the limits for both the numerator and denominator exist and neither is zero; so L’Hospital’s rule does not apply. In fact, all we have to do is use properties of limits. For then we see that limit = 3 . 002 10.0 points When f, g, F and G are functions such that lim x → 1 f ( x ) = 0 , lim x → 1 g ( x ) = 0 , lim x → 1 F ( x ) = 2 , lim x → 1 G ( x ) = ∞ , which, if any, of A. lim x → 1 f ( x ) g ( x ) ; B. lim x → 1 g ( x ) G ( x ) ; C. lim x → 1 f ( x ) g ( x ) ; are indeterminate forms? 1. C only 2. A and B only 3. none of them 4. A and C only correct 5. all of them 6. B and C only 7. B only 8. A only Explanation: A. Since lim x → 1 f ( x ) g ( x ) = , this limit is an indeterminate form. B. By properties of limits lim x → 1 g ( x ) G ( x ) = ∞ = 0 , so this limit is not an indeterminate form. C. Since lim x → 1 f ( x ) g ( x ) = 0 , this limit is an indeterminate form. 003 10.0 points lawrence (cdl678) – Homework 1 – Odell – (56280) 2 When f, g, F and G are functions such that lim x → 1 f ( x ) = 0 , lim x → 1 g ( x ) = 0 , lim x → 1 F ( x ) = 2 , lim x → 1 G ( x ) = ∞ , which, if any, of A. lim x → 1 F ( x ) g ( x ) ; B. lim x → 1 g ( x ) G ( x ) ; C. lim x → 1 f ( x ) g ( x ) ; are NOT indeterminate forms? 1. A and C only 2. all of them 3. none of them 4. B only 5. A and B only 6. A only correct 7. B and C only 8. C only Explanation: A. By properties of limits lim x → 1 F ( x ) g ( x ) = 2 = 1 , so this limit is not an indeterminate form. B. Since lim x → 1 = ∞· , this limit is an indeterminate form. C. Since lim x → 1 f ( x ) g ( x ) = , this limit is an indeterminate form. 004 10.0 points When f, g, F and G are functions such that lim x → 1 f ( x ) = 0 , lim x → 1 g ( x ) = ∞ , lim x → 1 F ( x ) = 2 , lim x → 1 G ( x ) = ∞ , which, if any, of A. lim x → 1 f ( x ) F ( x ) g ( x ) , B. lim x → 1 G ( x ) f ( x ) , C. lim x → 1 f ( x ) F ( x ) , are NOT indeterminate forms? 1. C only 2. A only 3. none of them 4. B and C only 5. A and B only 6. B only 7. all of them 8. A and C only correct Explanation: A. By properties of limits, lim x → 1 f ( x ) F ( x ) g ( x ) = · 2 ∞ = 0 , so this limit is not an indeterminate form....
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 Spring '10
 odell
 Limit, lim, Limit of a function, Indeterminate form, Extended real number line

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