{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Assignment 7

# Assignment 7 - patino(mp25752 Assignment7 luecke(57510 This...

This preview shows pages 1–3. Sign up to view the full content.

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 0 r ( t ) dt when r ( t ) = (Big 4 1 + t 2 , 2 t 1 + t 2 , 4 (1 + t ) 2 )Big . 1. I = ( π, 2 , 2 ln 2 ) 2. I = ( ln 2 , π, 2 ) 3. I = ( π, ln 2 , 2 ) correct 4. I = ( 4 , 2 π, 4 ln 2 ) 5. I = ( 4 ln2 , 2 , 4 π ) 6. I = ( 4 , ln 2 , 4 π ) Explanation: For a vector function r ( t ) = ( f ( t ) , g ( t ) , h ( t ) ) , the components of the vector I = integraldisplay 1 0 r ( t ) dt are given by integraldisplay 1 0 f ( t ) dt, integraldisplay 1 0 g ( t ) dt, integraldisplay 1 0 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 0 f ( t ) dt = integraldisplay 1 0 4 1 + t 2 dt = bracketleftBig 4 tan 1 t bracketrightBig 1 0 = π , while integraldisplay 1 0 g ( t ) dt = integraldisplay 1 0 2 t 1 + t 2 dt = bracketleftBig ln(1 + t 2 ) bracketrightBig 1 0 = ln 2 , and integraldisplay 1 0 h ( t ) dt = integraldisplay 1 0 4 (1 + t ) 2 dt = bracketleftBig 4 1 + t bracketrightBig 1 0 = 2 . Consequently, I = ( π, 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 ,

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 ). 1. r ′′ ( t ) = (big 1 , 8 t 6 , 5 t 3 )big 2. r ′′ ( t ) = (big 1 , 56 t 6 , 20 t 3 )big 3. r ′′ ( t ) = (big 1 , 8 t 7 , 5 t 4 )big 4. r ′′ ( t ) = (big 0 , 56 t 6 , 20 t 3 )big correct 5. r ′′ ( t ) = (big 0 , 56 t 7 , 20 t 4 )big 6. r ′′ ( t ) = (big 0 , 8 t 6 , 5 t 3 )big Explanation: For a vector function r ( t ) = ( f ( t ) , g ( t ) , h ( t ) ) ,
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online