Assignment 7 - patino (mp25752) Assignment7 luecke (57510)...

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Unformatted text preview: patino (mp25752) Assignment7 luecke (57510) 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Determine the vector I = integraldisplay 1 r ( t ) dt when r ( t ) = (Big 4 1 + t 2 , 2 t 1 + t 2 , 4 (1 + t ) 2 )Big . 1. I = ( , 2 , 2 ln2 ) 2. I = ( ln2 , , 2 ) 3. I = ( , ln2 , 2 ) correct 4. I = ( 4 , 2 , 4 ln2 ) 5. I = ( 4 ln2 , 2 , 4 ) 6. I = ( 4 , ln 2 , 4 ) Explanation: For a vector function r ( t ) = ( f ( t ) , g ( t ) , h ( t ) ) , the components of the vector I = integraldisplay 1 r ( t ) dt are given by integraldisplay 1 f ( t ) dt, integraldisplay 1 g ( t ) dt, integraldisplay 1 h ( t ) dt , respectively. But when r ( t ) = (Big 4 1 + t 2 , 2 t 1 + t 2 , 4 (1 + t ) 2 )Big , we see that integraldisplay 1 f ( t ) dt = integraldisplay 1 4 1 + t 2 dt = bracketleftBig 4 tan 1 t bracketrightBig 1 = , while integraldisplay 1 g ( t ) dt = integraldisplay 1 2 t 1 + t 2 dt = bracketleftBig ln(1 + t 2 ) bracketrightBig 1 = ln 2 , and integraldisplay 1 h ( t ) dt = integraldisplay 1 4 (1 + t ) 2 dt = bracketleftBig 4 1 + t bracketrightBig 1 = 2 . Consequently, I = ( , ln 2 , 2 ) . 002 10.0 points Find the derivative of r ( t ) = a + t b + t 6 c . 1. r ( t ) = a + b 6 t 5 c 2. r ( t ) = a + b + 6 t 5 c 3. r ( t ) = a + b + t 5 c 4. r ( t ) = b t 5 c 5. r ( t ) = b + 6 t 5 c correct Explanation: The derivative of r ( t ) = a + t b + t 6 c with respect to t is the sum of the derivatives of each of the terms. Thus, since d dt ( a ) = 0, d dt ( t b ) = b , patino (mp25752) Assignment7 luecke (57510) 2 and d dt ( t 6 c ) = 6 t 6 1 c = 6 t 5 c , then r ( t ) = b + 6 t 5 c . keywords: Stewart5e, vector function, deriva- tive, 003 10.0 points If r ( t ) = (big t, t 8 , t 5 )big , find r ( t )....
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This note was uploaded on 10/21/2009 for the course M 53215 taught by Professor Lueke during the Spring '09 term at University of Texas at Austin.

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Assignment 7 - patino (mp25752) Assignment7 luecke (57510)...

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