9 - trevino ochoa (dt23653) HW09 mostovyi (54020) This...

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trevino ochoa (dt23653) – HW09 – mostovyi – (54020)1Thisprint-outshouldhave20questions.Multiple-choice questions may continue onthe next column or page – find all choicesbefore answering.00110.0pointsFrom the contour map offshown belowdecide whetherfx, fyare positive, negative,or zero atP.00-2-2-4-4-6-6Pxy1.fx>0,fy<02.fx>0,fy= 03.fx<0,fy>04.fx>0,fy>05.fx<0,fy<06.fx<0,fy= 0correctExplanation:When we walk in thex-direction fromPweare walking downhill, sofx<0. On the otherhand, when we walk in they-direction fromPour elevation doesn’t change because we arewalking along a contour, sofy= 0.Consequently, atPfx<0,fy= 0.keywords: contour map, slope, partial deriva-tive,00210.0pointsDeterminefxwhenf(x , y) = (x2+y)(2y2-x).1.fx=y-4xy2-3x22.fx= 2y-2xy2+ 3x23.fx= 4xy2+y-3x24.fx= 2xy2-2y+ 3x25.fx= 2y+ 2xy2+ 3x26.fx= 4xy2-y-3x2correctExplanation:From the Product Rule we see thatfx= 2x(2y2-x)-(x2+y).Consequently,fx= 4xy2-y-3x2.00310.0pointsDeterminefywhenf(x, y) = sin(4x-y)-ycos(4x-y).1.fy=-2 cos(4x-y)-ysin(4x-y)correct2.fy=ycos(4x-y)3.fy= 2 sin(4x-y)-ycos(4x-y)4.fy= 2 cos(4x-y) +ysin(4x-y)5.fy=ysin(4x-y)6.fy=-ycos(4x-y)
trevino ochoa (dt23653) – HW09 – mostovyi – (54020)27.fy=-ysin(4x-y)8.fy=-2 sin(4x-y) +ycos(4x-y)fx= 8x+xy,fy= 8y+x23.fx= 8x+ 2x,fy= 8y+x200410.0pointsFind the slope in thex-direction at the2.fx= 8x+xy,fy= 8y+x23.fx= 8x+ 2x,fy= 8y+x2
pointP(0,2, f(0,2)) on the graph offwhenf(x, y) = 2(2x+y)e-xy.1.slope =-62.slope =-4correct3.slope =-84.slope =-105.slope =-2On the other hand,differentiatingf(x, y)with respect toyholdingxfixed, we see thatfy= 8y+x2.00610.0pointsFind the value offxat (2,1) whenf(x, y) = 5x3-2x2y-7x+ 2y.

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Term
Spring
Professor
RAdin
Tags
Derivative, Slope, trevino ochoa

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