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Unformatted text preview: wtm369 – Homework 10 – Helleloid – (58250) 1 This printout should have 18 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 3) 10.0 points A certain function f is given by the graph 4 8 − 4 − 8 4 − 4 − 8 (i) What is the value of lim x →−∞ f ( x ) 1. limit = 2 2. limit does not exist 3. limit = − 3 4. limit = 3 correct 5. limit = − 2 Explanation: To the left of x = − 2 the graph of f os cillates about the line y = 3 and as x ap proaches −∞ the oscillations become smaller and smaller. Thus limit = 3 . 002 (part 2 of 3) 10.0 points (ii) What is the value of lim x →∞ f ( x )? 1. limit does not exist 2. limit = 2 3. limit = − 2 correct 4. limit = 3 5. limit = − 3 Explanation: To the right of x = 1 the graph of f is asymptotic to the line y = − 2. Thus limit = − 2 . 003 (part 3 of 3) 10.0 points (iii) What is the value of lim x →− 2 f ( x )? 1. limit = 2 2. limit = 3 3. limit = − 3 4. limit = ∞ correct 5. limit = − 2 Explanation: From the graph of f the left hand limit lim x →− 2 − f ( x ) = ∞ , while the right hand limit lim x →− 2+ f ( x ) = ∞ . Thus the twosided limit lim x →− 2 f ( x ) = ∞ . 004 10.0 points wtm369 – Homework 10 – Helleloid – (58250) 2 Determine if the limit lim x →∞ 2 x + 1 x 2 − 3 x + 2 exists, and if it does, find its value. 1. limit = 1 2. limit = 2 3. limit = 1 2 4. limit = 0 correct 5. limit = − 2 3 6. limit doesn’t exist Explanation: Dividing in the numerator and denominator by x 2 , the highest power, we see that 2 x + 1 x 2 − 3 x + 2 = 2 x + 1 x 2 1 − 3 x + 2 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 . 005 10.0 points Determine lim x →∞ 7 x 2 − 6 x + 5 5 + x − 3 x 2 . 1. limit = 7 6 2. limit = 0 3. limit = − 7 3 correct 4. limit = ∞ 5. none of the other answers Explanation: Dividing the numerator and denominator by x 2 we see that 7 x 2 − 6 x + 5 5 + x − 3 x 2 = 7 − 6 x + 5 x 2 5 x 2 + 1 x − 3 . On the other hand, lim x →∞ 1 x = lim x →∞ 1 x 2 = 0 . By Properties of limits, therefore, the limit = − 7 3 . 006 10.0 points Determine if the limit lim x →−∞ √ x 2 + 4 x 4 x + 5 exists, and if it does, find its value. 1. limit = − 1 2. limit = 1 3. limit = 4 5 4. limit = − 4 5 5. limit does not exist 6. limit = − 1 4 correct 7. limit = 1 4 Explanation: Since √ x 2 =  x  , ( √ a is always non negative, remember), the given expression can be written as √ x 2 + 4 x 4 x + 5 =  x  x parenleftBig radicalbig 1 + 4 /x 4 + 5 /x parenrightBig . wtm369 – Homework 10 – Helleloid – (58250) 3 But lim x →−∞ radicalbigg 1 + 4 x = 1 , lim x →−∞ parenleftBig 4+ 5 x parenrightBig = 4 ....
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 Fall '08
 schultz
 Calculus, Limit, lim, Mathematical analysis, Limit of a function

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