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Unformatted text preview: syed (sms3768) Quest HW 10 seckin (56425) 1 This printout should have 12 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Determine if the limit lim x 2 x + 3 x 2 x + 4 exists, and if it does, find its value. 1. limit = 3 2. limit doesnt exist 3. limit = 4 4. limit = 2 5. limit = 3 4 6. limit = 0 correct Explanation: Dividing in the numerator and denominator by x 2 , the highest power, we see that 2 x + 3 x 2 x + 4 = 2 x + 3 x 2 1 1 x + 4 x 2 . On the other hand, lim x 1 x = lim x 1 x 2 = 0 . By Properties of limits, therefore, the limit exists and limit = 0 . 002 10.0 points Determine if lim x parenleftbigg 2 x x 1 + 5 x x + 1 parenrightbigg exists, and if it does, find its value. 1. limit = 4 2. limit = 8 3. limit = 7 correct 4. limit = 6 5. limit = 5 6. limit does not exist Explanation: Bringing the expression to a common de nominator, we see that 2 x x 1 + 5 x x + 1 = 2 x ( x + 1) + 5 x ( x 1) ( x 1)( x + 1) = 7 x 2 3 x x 2 1 . Thus after dividing through by x 2 we see that lim x parenleftbigg 2 x x 1 + 5 x x + 1 parenrightbigg = lim x 7 3 x 1 1 x 2 . Consequently, the limit exists and limit = 7 . 003 10.0 points Determine if the limit lim x x 2 + 3 x 3 x + 4 exists, and if it does, find its value. 1. limit = 1 2. limit does not exist 3. limit = 3 4 syed (sms3768) Quest HW 10 seckin (56425) 2 4. limit = 3 4 5. limit = 1 6. limit = 1 3 correct 7. limit = 1 3 Explanation: Since x 2 =  x  , ( a is always non negative, remember), the given expression can be written as x 2 + 3 x 3 x + 4 =  x  x parenleftBig radicalbig 1 + 3 /x 3 + 4 /x parenrightBig . But lim x radicalbigg 1 + 3 x = 1 , lim x parenleftBig 3+ 4 x parenrightBig = 3 . On the other hand, lim x  x  x = 1 . Consequently, by Properties of Limits, the given limit exists, and limit = 1 3 . 004 10.0 points Use intercepts and asymptotes to decide which of the following functions has as its graph....
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 Spring '10
 seckin

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