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Unformatted text preview: husain (aih243) HW08 Gilbert (56215) 1 This printout should have 22 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 = 1 2. limit = 2 3. limit = 1 4. limit does not exist 5. limit = 2 correct Explanation: To the left of x = 2 the graph of f os cillates about the line y = 2 and as x ap proaches the oscillations become smaller and smaller. Thus limit = 2 . 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 = 1 correct 3. limit = 1 4. limit = 2 5. limit = 2 Explanation: To the right of x = 1 the graph of f is asymptotic to the line y = 1. Thus limit = 1 . 003 (part 3 of 3) 10.0 points (iii) What is the value of lim x 2 f ( x )? 1. limit = 1 2. limit = 2 3. limit = correct 4. limit = 1 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 husain (aih243) HW08 Gilbert (56215) 2 Determine if the limit lim x 3 x + 1 x 2 x + 5 exists, and if it does, find its value. 1. limit = 1 5 2. limit = 0 correct 3. limit doesnt exist 4. limit = 1 5. limit = 5 6. limit = 3 Explanation: Dividing in the numerator and denominator by x 2 , the highest power, we see that 3 x + 1 x 2 x + 5 = 3 x + 1 x 2 1 1 x + 5 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 if the limit lim x x 2 + 5 x 5 x + 3 exists, and if it does, find its value. 1. limit does not exist 2. limit = 5 3 3. limit = 1 4. limit = 1 5 correct 5. limit = 5 3 6. limit = 1 7. limit = 1 5 Explanation: Since x 2 =  x  , ( a is always non negative, remember), the given expression can be written as x 2 + 5 x 5 x + 3 =  x  x parenleftBig radicalbig 1 + 5 /x 5 + 3 /x parenrightBig . But lim x radicalbigg 1 + 5 x = 1 , lim x parenleftBig 5+ 3 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 . 006 10.0 points Use intercepts and asymptotes to decide which of the following functions has husain (aih243) HW08 Gilbert (56215) 3 as its graph. 1. f ( x ) = 3 x x + 3 2. f ( x ) = x + 3 x 3 3. f ( x ) = x 3 x + 3 correct 4. f ( x ) = x + 3 x + 3 5. f ( x ) = x 3 x 3 Explanation: The graph of any function f ( x ) = ax b x + c has the properties (i) a horizontal asymptote y = a , (ii) a vertical asymptote x = c , (iii) an xintercept at x = b a...
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 Spring '06
 McAdam

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