12.01310.0pointsFind the domain of the functionf(x, y) = ln(2-x2-7y2).1.(x, y) :12x2+72y2>1Determine the volume,V, of the box as afunction ofxandy.

keywords: function several variables, ln func-tion, domain01410.0pointsA 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 figurexxxxxxxx

01510.0pointsWhich of the following surfaces could havecontour map0123451.parabolic cylinderWhich one of the following could be thecontour map of a parabolic cylinder?1.0123123-1-2-3-1-2-32.0123452.paraboloidcorrect3.cone4.hyperbolic paraboloid5.planeExplanation:The graphs in the contour map show thatthe horizontal cross-sections of the surface areall circles as in cones and paraboloids. On theother hand, the values of the contours and thegrid show that these cross-sections grow in-creasingly fast. This occurs for a paraboloid,but not for a cone.Consequently, of the surfaces listed, theonly one having the given contour map is aparaboloid.01234512345cor-rect

10.0points3.01234512345cor-rect

liang (xl5432) – HW11 – berg – (55120)94.0123455.1023Explanation:The horizontal cross-sections of a paraboliccylinder are always parallel lines, just as theyare for a plane. This eliminates all but two ofthe contour maps. But for a parabolic cylin-der, these parallel lines will beincreasinglyclosetogether when the parabola of cross-section opens upwards.Consequently,of the five given contourmaps only01234512345couldbethecontourmapofaparabolic cylinder.keywords:contour map, conic section, hy-perbolic paraboloid, cone, plane, paraboliccylinder, paraboloid,1.2.zxy

01710.0pointsWhich of the following surfaces could havecontour map0-112

xzy

liang (xl5432) – HW11 – berg – (55120)10