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everts (cce382) – homework 4 – luecke – (55550)1Thisprint-outshouldhave15questions.Multiple-choice questions may continue onthe next column or page – find all choicesbefore answering.00110.0pointsFind the domain of the functionf(x,y) = ln(7-x2-5y2).1.braceleftBig(x, y) :17x2+57y2≤1bracerightBigxxxxxxxxDetermine the volume,V, of the box as afunction ofxandy.(x, y) :1x2+5y2<1bracerightBig.
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77keywords: function several variables, ln func-tion, domain00210.0pointsA rectangular piece of cardboard is 3 timesas long as it is wide.If the length of theshorter side isyinches and an open box isconstructed by cutting equal squares of side-lengthxinches from the corners of the piece ofcardboard and turning up the sides as shownin the figureV(x) = (length)×(width)×(height)=x(3y-2x)(y-2x).Consequently,V(x) = 3xy2-8x2y+ 4x3cu. ins.00310.0pointsWhich one of the following functions has
everts (cce382) – homework 4 – luecke – (55550)2-2-1012x-2-1012y02468z-2-1012x-2-101202468as its graph.1.f(x,y) =12(8-x2-y2)2.f(x,y) = 2x23.f(x,y) =12(x2+y2)4.f(x,y) =y2-x25.f(x,y) = 2y2correctExplanation:The cross-section of the graph by the planey= 0 gives a straight line parallel to thex-yplane, indicating that the function does not