Quest HW 10

# Quest HW 10 - roberts(eer474 – Quest HW 10 – seckin...

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Unformatted text preview: roberts (eer474) – Quest HW 10 – seckin – (56425) 1 This print-out should have 12 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 →∞ x + 4 x 2 − 2 x + 3 exists, and if it does, find its value. 1. limit doesn’t exist 2. limit = 4 3. limit = 0 correct 4. limit = 3 5. limit = − 1 2 6. limit = 4 3 Explanation: Dividing in the numerator and denominator by x 2 , the highest power, we see that x + 4 x 2 − 2 x + 3 = 1 x + 4 x 2 1 − 2 x + 3 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 3 x x − 1 + 4 x x + 1 parenrightbigg exists, and if it does, find its value. 1. limit = 3 2. limit does not exist 3. limit = 4 4. limit = 7 correct 5. limit = 5 6. limit = 6 Explanation: Bringing the expression to a common de- nominator, we see that 3 x x − 1 + 4 x x + 1 = 3 x ( x + 1) + 4 x ( x − 1) ( x − 1)( x + 1) = 7 x 2 − x x 2 − 1 . Thus after dividing through by x 2 we see that lim x →−∞ parenleftbigg 3 x x − 1 + 4 x x + 1 parenrightbigg = lim x →−∞ 7 − 1 x 1 − 1 x 2 . Consequently, the limit exists and limit = 7 . 003 10.0 points Determine if the limit lim x →−∞ √ x 2 + 5 x 5 x + 2 exists, and if it does, find its value. 1. limit = 1 5 2. limit = − 1 3. limit does not exist roberts (eer474) – Quest HW 10 – seckin – (56425) 2 4. limit = 5 2 5. limit = 1 6. limit = − 1 5 correct 7. limit = − 5 2 Explanation: Since √ x 2 = | x | , ( √ a is always non- negative, remember), the given expression can be written as √ x 2 + 5 x 5 x + 2 = | x | x parenleftBig radicalbig 1 + 5 /x 5 + 2 /x parenrightBig . But lim x →−∞ radicalbigg 1 + 5 x = 1 , lim x →−∞ parenleftBig 5+ 2 x parenrightBig = 5 . On the other hand, lim x →−∞ | x | x = − 1 . Consequently, by Properties of Limits, the given limit exists, and limit = − 1 5 . 004 10.0 points Use intercepts and asymptotes to decide which of the following functions has as its graph. 1. f ( x ) = x + 3 x − 2 2. f ( x ) = 3 − x x + 2 3. f ( x ) = x − 3 x − 2 4. f ( x ) = x + 3 x + 2 5. f ( x ) = x − 3 x + 2 correct Explanation: The graph of any function f ( x ) = ax − b x + c has the properties (i) a horizontal asymptote...
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Quest HW 10 - roberts(eer474 – Quest HW 10 – seckin...

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