Homework 4.pdf - Heather Macgregor Assignment Homework 4...

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Heather Macgregor MATH6A-03-S18-Martinez Assignment Homework 4 due 05/30/2018 at 11:30pm PDT 1. (1 pt) Find the maximum and minimum values of f ( x , y ) = 4 x + y on the ellipse x 2 + 4 y 2 = 1 maximum value: minimum value: Answer(s) submitted: 4(8/sqrt(65)) + (1/(2*sqrt(65))) -4(8/sqrt(65)) - (1/(2*sqrt(65))) (correct) 2. (1 pt) Find the maximum and minimum values of the func- tion f ( x , y , z ) = x + 2 y subject to the constraints y 2 + z 2 = 144 and x + y + z = 10. Maximum value is , occuring at ( , , ). Minimum value is , occuring at ( , , ). Answer(s) submitted: 10+12*sqrt(2) 10 6sqrt2 -6sqrt2 10-12sqrt2 10 -6sqrt2 6sqrt2 (correct) 3. (1 pt) Find the absolute maximum and minimum of the function f ( x , y ) = x 2 - y 2 subject to the constraint x 2 + y 2 = 256. As usual, ignore unneeded answer blanks, and list points in lexicographic order. Absolute minimum value: attained at ( , ) and ( , ). Absolute maximum value: attained at ( , ) and ( , ). Answer(s) submitted: -256 0 -16 0 16 256 -16 0 16 0 (correct) 4. (1 pt) Find the arclength of the curve r ( t ) = h 9 2 t , e 9 t , e - 9 t i , 0 t 1 Answer(s) submitted: eˆ9 - (1/eˆ9) (correct) 5. (1 pt) Consider the path r ( t ) = ( 12 t , 6 t 2 , 6ln t ) defined for t > 0. Find the length of the curve between the points ( 12 , 6 , 0 ) and ( 60 , 150 , 6ln ( 5 )) . Answer(s) submitted: 153.66 (correct) 6. (1 pt) Find the length of the given curve: r ( t ) = ( 5 t , - 4sin t , - 4cos t ) where - 2 t 5. Answer(s) submitted: 7sqrt(41) (correct) 7. (1 pt) Find the arclength of the curve r ( t ) = h 10sin t , - 9 t , 10cos t i , - 3 t 3 Answer(s) submitted: 6sqrt(181) (correct) 8.
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