HW10-solutions-1 - zakaria(mmz255 – HW10 – gilbert...

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Unformatted text preview: zakaria (mmz255) – HW10 – gilbert – (55485) 1 This print-out should have 17 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(6- x 2- 3 y 2 ) . 1. braceleftBig ( x, y ) : 1 6 x 2 + 1 2 y 2 > 1 bracerightBig 2. braceleftBig ( x, y ) : 1 3 x 2 + 1 6 y 2 > 1 bracerightBig 3. braceleftBig ( x, y ) : 1 3 x 2 + 1 6 y 2 < 1 bracerightBig 4. braceleftBig ( x, y ) : 1 6 x 2 + 1 2 y 2 < 1 bracerightBig correct 5. braceleftBig ( x, y ) : 1 3 x 2 + 1 6 y 2 ≤ 1 bracerightBig 6. braceleftBig ( x, y ) : 1 6 x 2 + 1 2 y 2 ≤ 1 bracerightBig Explanation: Since ln x is defined only for x > 0, the function f ( x, y ) = ln(6- x 2- 3 y 2 ) is defined only for braceleftBig ( x, y ) : 1 6 x 2 + 1 2 y 2 < 1 bracerightBig . keywords: function several variables, ln func- tion, domain 002 10.0 points Find the domain of the function f ( x, y ) = radicalbig x 2 + 4 y 2- 7 . 1. braceleftBig ( x, y ) : 1 7 x 2 + 4 7 y 2 ≥ 1 bracerightBig correct 2. braceleftBig ( x, y ) : 1 4 x 2 + 1 7 y 2 > 1 bracerightBig 3. braceleftBig ( x, y ) : 1 4 x 2 + 1 7 y 2 ≥ 1 bracerightBig 4. braceleftBig ( x, y ) : 1 7 x 2 + 4 7 y 2 < 1 bracerightBig 5. braceleftBig ( x, y ) : 1 4 x 2 + 1 7 y 2 < 1 bracerightBig 6. braceleftBig ( x, y ) : 1 7 x 2 + 4 7 y 2 > 1 bracerightBig Explanation: Since √ x is defined only for x ≥ 0, the function f ( x, y ) = radicalbig x 2 + 4 y 2- 7 is defined only for braceleftBig ( x, y ) : 1 7 x 2 + 4 7 y 2 ≥ 1 bracerightBig . keywords: function several variables, square root function, domain 003 10.0 points A rectangular piece of cardboard is 3 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 . zakaria (mmz255) – HW10 – gilbert – (55485) 2 1. V ( x, y ) = 3 xy 2- 8 x 2 y- 4 x 3 cu. ins 2. V ( x, y ) = 8 xy 2 + 3 x 2 y- 4 x 3 cu. ins 3. V ( x, y ) = 3 xy 2- 8 x 2 y +4 x 3 cu. ins cor- rect 4. V ( x, y ) = 8 xy 2- 3 x 2 y + 2 x 3 cu. ins 5. V ( x, y ) = 3 xy 2 + 8 x 2 y + 2 x 3 cu. ins 6. V ( x, y ) = 8 xy 2 + 3 x 2 y- 2 x 3 cu. ins Explanation: The rectangular sheet of cardboard will have dimensions y × 3 y . Thus the length...
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This note was uploaded on 06/05/2011 for the course MATH 408 D taught by Professor Gilbert during the Spring '11 term at University of Texas.

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HW10-solutions-1 - zakaria(mmz255 – HW10 – gilbert...

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