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# exam 1 - Version 095 Exam 1 Radin(56520 This print-out...

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Version 095 – Exam 1 – Radin – (56520) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points Below is the graph oF a Function f . 2 4 6 2 4 6 2 4 6 8 2 4 Use the graph to determine lim x 4 f ( x ) . 1. limit does not exist correct 2. limit = 3 3. limit = 7 4. limit = 9 5. limit = 4 Explanation: ±rom the graph it is clear the f has a leFt hand limit at x = 4 which is equal to 3; and a right hand limit which is equal to 0. Since the two numbers do not coincide, the limit does not exist . 002 10.0 points Determine iF lim x 0 1 7 x sin x exists, and iF it does, fnd its value. 1. limit = correct 2. none oF the other answers 3. limit = 1 7 4. limit = −∞ 5. limit = 1 7 Explanation: Since 1 7 x sin x > 0 For all small x n = 0, both positive and negative, while lim x 0 x sin x = 0 , we see that lim x 0 1 7 x sin x = . 003 10.0 points Determine iF lim x 0 1 x 1 + x x exists, and iF it does, fnd its value. 1. limit = 1 2 2. limit does not exist 3. limit = 1 correct 4. limit = 2 5. limit = 2 6. limit = 1 2 7. limit = 1 Explanation:

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Version 095 – Exam 1 – Radin – (56520) 2 After rationalization we see that 1 x 1 + x = (1 x ) (1 + x ) 1 x + 1 + x = 2 x 1 x + 1 + x . Thus 1 x 1 + x x = 2 1 x + 1 + x for all x n = 0. But lim x 0 ( 1 x + 1 + x ) = 2 . Consequently, by Properties of Limits, limit = 2 2 = 1 . 004 10.0 points Determine if lim x 4+ 3 x 2 10 x 8 | x 4 | exists, and if it does, Fnd its value. 1. limit does not exist 2. limit = 14 correct 3. limit = 14 4. limit = 10 5. limit = 10 Explanation: After factorization, 3 x 2 10 x 8 = (3 x + 2)( x 4) . Thus 3 x 2 10 x 8 | x 4 | = (3 x + 2) p x 4 | x 4 | P But x 4 | x 4 | = 1 , x > 4, DNE , x = 4, 1 , x < 4 , while lim x 4+ (3 x + 2) = 14 . Consequently, by properties of limits, lim x 4+ 3 x 2 10 x 8 | x 4 | = 14 . 005 10.0 points ±ind the value of lim x 0 sin 2 6 x 2 x 2 4 x 2 if the limit exists. 1.
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exam 1 - Version 095 Exam 1 Radin(56520 This print-out...

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