HW 01-solutions

# HW 01-solutions - gonzales (pag757) HW 01 Odell (57000) 1...

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Unformatted text preview: gonzales (pag757) HW 01 Odell (57000) 1 This print-out should have 30 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Determine if lim x 1 parenleftBig 4 x 2 + 3 x 2 + 1 parenrightBig exists, and if it does, find its value. 1. limit does not exist 2. limit = 3 3. limit = 7 2 correct 4. limit = 4 5. limit = 7 Explanation: Set f ( x ) = 4 x 2 + 3 , g ( x ) = x 2 + 1 . Then lim x 1 f ( x ) = 7 , lim x 1 g ( x ) = 2 . Thus the limits for both the numerator and denominator exist and neither is zero; so LHospitals rule does not apply. In fact, all we have to do is use properties of limits. For then we see that limit = 7 2 . 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. A and C only 2. C only correct 3. all of them 4. A and B only 5. B and C only 6. A only 7. B only 8. none of them Explanation: A. By properties of limits lim x 1 F ( x ) g ( x ) = 2 = 1 , so this limit is not 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 ) = , this limit is an indeterminate form. 003 10.0 points gonzales (pag757) HW 01 Odell (57000) 2 When f, g, F and G are functions such that lim x 2 f ( x ) = 0 , lim x 2 g ( x ) = 1 , lim x 2 F ( x ) = 2 , lim x 2 G ( x ) = , which of the following is an indeterminate form? 1. lim x 2 g ( x ) G ( x ) correct 2. lim x 2 F ( x ) G ( x ) 3. lim x 2 F ( x ) f ( x ) 4. lim x 2 f ( x ) g ( x ) 5. lim x 2 g ( x ) F ( x ) Explanation: Since lim x 2 g ( x ) G ( x ) = 1 , lim x 2 F ( x ) G ( x ) = 2 , lim x 2 f ( x ) g ( x ) = 0 1 , lim x 2 g ( x ) F ( x ) = 1 2 , lim x 2 F ( x ) f ( x ) = 2 , we see that only lim x 2 g ( x ) G ( x ) is an indeterminate form. 004 10.0 points Determine the value of lim x x x 2 + 7 . 1. limit = 1 2 2. limit = 2 3. limit = 0 4. limit = 5. limit = 4 6. limit = 1 4 7. limit = 1 correct Explanation: Since lim x x x 2 + 7 , the limit is of indeterminate form. We might first try to use LHospitals Rule lim x f ( x ) g ( x ) = lim x f ( x ) g ( x ) with f ( x ) = x , g ( x ) = radicalbig x 2 + 7 to evaluate the limit. But f ( x ) = 1 , g ( x ) = x x 2 + 7 , so lim x f ( x ) g ( x ) = lim x x 2 + 7 x = , which is again of indeterminate form. Lets try using LHospitals Rule again but now with f ( x ) = radicalbig x 2 + 7 , g ( x ) = x , and f ( x ) = x x 2 + 7 , g ( x ) = 1 ....
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## This note was uploaded on 10/28/2009 for the course M 57000 taught by Professor Odell during the Fall '09 term at University of Texas at Austin.

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HW 01-solutions - gonzales (pag757) HW 01 Odell (57000) 1...

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