M408m-Luecke_HW4 - romasko (qrr58) – Assignment 4 –...

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Unformatted text preview: romasko (qrr58) – Assignment 4 – luecke – (55035) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find the domain of the function f ( x, y ) = ln(7- x 2- 6 y 2 ) . 1. braceleftBig ( x, y ) : 1 7 x 2 + 6 7 y 2 < 1 bracerightBig correct 2. braceleftBig ( x, y ) : 1 6 x 2 + 1 7 y 2 ≤ 1 bracerightBig 3. braceleftBig ( x, y ) : 1 7 x 2 + 6 7 y 2 > 1 bracerightBig 4. braceleftBig ( x, y ) : 1 7 x 2 + 6 7 y 2 ≤ 1 bracerightBig 5. braceleftBig ( x, y ) : 1 6 x 2 + 1 7 y 2 < 1 bracerightBig 6. braceleftBig ( x, y ) : 1 6 x 2 + 1 7 y 2 > 1 bracerightBig Explanation: Since ln x is defined only for x > 0, the function f ( x, y ) = ln(7- x 2- 6 y 2 ) is defined only for braceleftBig ( x, y ) : 1 7 x 2 + 6 7 y 2 < 1 bracerightBig . keywords: function several variables, ln func- tion, domain 002 10.0 points A rectangular piece of cardboard is 4 times as long as it is wide. If the length of the shorter side is y inches and an open box is constructed by cutting equal squares of side- length x inches from the corners of the piece of cardboard and turning up the sides as shown in the figure x x x x x x x x determine the volume, V , of the box as a function of x and y . 1. V ( x, y ) = 4 xy 2 + 10 x 2 y + 2 x 3 cu. ins 2. V ( x, y ) = 10 xy 2 + 4 x 2 y- 4 x 3 cu. ins 3. V ( x, y ) = 4 xy 2- 10 x 2 y- 4 x 3 cu. ins 4. V ( x, y ) = 10 xy 2 + 4 x 2 y- 2 x 3 cu. ins 5. V ( x, y ) = 10 xy 2- 4 x 2 y + 2 x 3 cu. ins 6. V ( x, y ) = 4 xy 2- 10 x 2 y + 4 x 3 cu. ins correct Explanation: The rectangular sheet of cardboard will have dimensions y × 4 y . Thus the length of the shorter side of the base of the box is y- 2 x , while the length of the longer side is 4 y- 2 x . Since the height of the box is x , the volume will thus be V ( x ) = (length) × (width) × (height) = x (4 y- 2 x )( y- 2 x ) ....
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This note was uploaded on 06/15/2011 for the course M 408M taught by Professor Gilbert during the Fall '07 term at University of Texas at Austin.

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M408m-Luecke_HW4 - romasko (qrr58) – Assignment 4 –...

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