This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 doesn’t 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....
View
Full Document
 Spring '10
 seckin
 lim, Mathematical analysis, Limit of a function, Quest HW

Click to edit the document details