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Unformatted text preview: Mahon, Kevin Homework 10 Due: Nov 3 2005, 3:00 am Inst: Edward Odell 1 This printout should have 18 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 3) 10 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 = 4 3. limit = 4 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 points (ii) What is the value of lim x f ( x )? 1. limit = 2 2. limit = 4 3. limit = 2 4. limit = 4 correct 5. limit does not exist Explanation: To the right of x = 1 the graph of f is asymptotic to the line y = 4. Thus limit = 4 . 003 (part 3 of 3) 10 points (iii) What is the value of lim x  2 f ( x )? 1. limit = correct 2. limit = 2 3. limit = 4 4. limit = 2 5. limit = 4 Explanation: From the graph of f the left hand limit lim x  2 f ( x ) = , Mahon, Kevin Homework 10 Due: Nov 3 2005, 3:00 am Inst: Edward Odell 2 while the right hand limit lim x  2+ f ( x ) = . Thus the twosided limit lim x  2 f ( x ) = . keywords: Stewart5e, 004 (part 1 of 1) 10 points Determine if the limit lim x  2 x x 1 + 6 x x + 1 exists, and if it does, find its value. 1. limit = 5 2. limit = 6 3. limit = 8 correct 4. limit = 4 5. limit = 7 6. limit doesnt exist Explanation: Bringing the expression to a common de nominator, we see that 2 x x 1 + 6 x x + 1 = 2 x ( x + 1) + 6 x ( x 1) ( x 1)( x + 1) = 8 x 2 4 x x 2 1 . Thus after dividing through by x 2 we see that lim x  2 x x 1 + 6 x x + 1 = lim x  8 4 x 1 1 x 2 . Consequently, the limit exists and lim x  2 x x 1 + 6 x x + 1 = 8 . keywords: Stewart5e, 005 (part 1 of 1) 10 points Determine if lim x x p 9 x 2 + 4 3 x exists, and if it does, find its value. 1. limit = 0 2. limit = 1 2 3. limit = 1 6 4. limit = 2 3 correct 5. limit does not exist 6. limit = 1 3 Explanation: After rationalization we see that x p 9 x 2 + 4 3 x = x 9 x 2 + 4 9 x 2 9 x 2 + 4 + 3 x = 4 x 9 x 2 + 4 + 3 x = 4 r 9 + 4 x 2 + 3 . On the other hand, lim x r 9 + 4 x 2 = 3 . Consequently, lim x x p 9 x 2 + 4 3 x Mahon, Kevin Homework 10 Due: Nov 3 2005, 3:00 am Inst: Edward Odell 3 exists and has limit = 2 3 . keywords: Stewart5e, limit, limit at infinity, square root function, rationalize numerator 006 (part 1 of 1) 10 points A certain function f is known to have the properties lim x  f ( x ) = 4 , lim x f ( x ) = 1 ....
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This homework help was uploaded on 04/15/2008 for the course M 408k taught by Professor Schultz during the Fall '08 term at University of Texas at Austin.
 Fall '08
 schultz
 Differential Calculus

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