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# calc10 - pokharel(yp624 HW10 Radin(56520 This print-out...

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pokharel (yp624) – HW10 – Radin – (56520) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Determine if the limit lim x → −∞ 3 + 2 x + 2 x 3 1 5 x 3 exists, and if it does, find its value. 1. limit does not exist 2. limit = 3 3. limit = 3 4. limit = 2 5 correct 5. limit = 2 5 Explanation: Dividing by x 3 in the numerator and de- nominator we see that 3 + 2 x + 2 x 3 1 5 x 3 = 3 x 3 + 2 x 2 + 2 1 x 3 5 . With s = 1 x , therefore, lim x → −∞ 3 + 2 x + 2 x 3 1 5 x 3 = lim s 0 3 s 3 + 2 s 2 + 2 s 3 5 . Consequently, the limit exists, and limit = 2 5 . 002 10.0 points Determine if lim x → −∞ parenleftbigg 4 x x 1 + 6 x x + 1 parenrightbigg exists, and if it does, find its value. 1. limit = 12 2. limit = 14 3. limit = 13 4. limit does not exist 5. limit = 10 correct 6. limit = 11 Explanation: Bringing the expression to a common de- nominator, we see that 4 x x 1 + 6 x x + 1 = 4 x ( x + 1) + 6 x ( x 1) ( x 1)( x + 1) = 10 x 2 2 x x 2 1 . Thus after dividing through by x 2 we see that lim x →−∞ parenleftbigg 4 x x 1 + 6 x x + 1 parenrightbigg = lim x →−∞ 10 2 x 1 1 x 2 . Consequently, the limit exists and limit = 10 . 003 10.0 points Determine if the limit lim x → −∞ x 2 + 7 x 7 x + 5 exists, and if it does, find its value. 1. limit = 1

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pokharel (yp624) – HW10 – Radin – (56520) 2 2. limit = 7 5 3. limit does not exist 4. limit = 1 5. limit = 7 5 6. limit = 1 7 7. limit = 1 7 correct Explanation: Since x 2 = | x | , ( a is always non- negative, remember), the given expression can be written as x 2 + 7 x 7 x + 5 = | x | x parenleftBig radicalbig 1 + 7 /x 7 + 5 /x parenrightBig . But lim x → −∞ radicalbigg 1 + 7 x = 1 , lim x → −∞ parenleftBig 7+ 5 x parenrightBig = 7 . On the other hand, lim x → −∞ | x | x = 1 . Consequently, by Properties of Limits, the given limit exists, and limit = 1 7 . 004 10.0 points Determine if lim x → ∞ parenleftBig radicalbig x 2 + 3 x parenrightBig exists, and if it does, find its value. 1. limit = 4 2. limit doesn’t exist 3. limit = 3 4. limit = 1 5. limit = 0 correct Explanation: After the rationalization radicalbig x 2 + 3 x = ( x 2 + 3) x 2 x 2 + 3 + x , we see that radicalbig x 2 + 3 x = 3 x 2 + 3 + x . On the other hand, lim x → ∞ 1 x 2 + 3 + x = 0 . Consequently, lim x → ∞ parenleftBig radicalbig x 2 + 3 x parenrightBig exists and limit = 0 . 005 10.0 points Determine if the limit lim x → ∞ x ( x + 6 x 4) exists, and find its value when it does. 1. limit = 0 2. limit = 2 3. limit = 1 4. limit = 5 correct 5. limit = 10 6. limit does not exist Explanation: By rationalization, x + 6 x 4 = ( x + 6) ( x 4) x + 6 + x 4 = 10 x + 6 + x 4 .
pokharel (yp624) – HW10 – Radin – (56520) 3 On the other hand, x x + 6 + x 4 = 1 radicalbigg 1 + 6 x + radicalbigg 1 4 x .

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calc10 - pokharel(yp624 HW10 Radin(56520 This print-out...

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