2200210261– 3::(100).1.(10) Consider the region bounded by the curvey=√x+ 1, thex-axis, and they-axis. LetVx,Vybe the volumes of the solid generated byrevolving the region about thex-axis and they-axis, respectively. Findthe ratioVx:Vy(Write it as simple as possible).2.(15)f(x, y) =x2y3x2+ 4y3,(x, y) = (0,0)0,(x, y) = (0,0).(a)Findfx(0,0) andfy(0,0).(b)Prove thatfis not continuous at the origin.3.(10) Find the maxima, minima, and saddle points off(x, y).f(x, y) = sinx+ siny+ sin(x+y).4.(10) Find the points on the curvexy+2xz= 5√5 nearest to the origin.5.(10) Let (0,0) be a critical point of a differentiable functionz=f(x, y).Does the condition “fxx>0 andfyy>0” imply thatfhas a localminimum at (0,0)? If not, find a counter example and a condition which
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