
#1
May709, 01:36 AM

P: 376

solved




#2
May709, 01:38 AM

P: 376

or if possible, be able to tell me, how to draw regions in maple? so i can at least picture it, and try to understand how to draw it.




#3
May709, 02:03 AM

P: 376

ok from that, i think i can see that x is from 0 to root(1y^2), y is from 0 to 1 and z is from 0 to 2y.. so they are bounds of my region.




#4
May709, 03:45 AM

P: 376

Vector Calculus, sketching regions in R3
please anyone?




#5
May709, 05:38 AM

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You have [itex]y\ge 0[/itex], [itex]0\le x^2+ y^2\le 1[/itex], [itex]z\le 2y[/itex] first draw an xyplane. [itex]y\ge 0[/itex] means your graph is in the upper half plane. the 0 in [itex]0\le x^2+ y^2\le 1[/itex] doesn't really tell us anything because [itex]x^2+ y^2[/itex] can't be negative anyway. But [itex]\x^2+ y^2= 1[/itex] is a circle with center at (0,0) and radius 1. Since y must be positive, draw the upper semicircle. Now draw a yzplane beside your xygraph. z= 2y is a line from (0,0) to (2, 1). If you now imagine that zaxis coming directly up from your first graph, with the yaxes aligned, you should see that plane forms a "top" on the parabolic cylinder. Yes, it is basically a "wedge" shape with the x= 0 plane forming one side, the plane top going down to cut the parabola. It is NOT a bounded region because there is no "bottom" unless you left out z= 0, say. 



#6
May709, 05:50 AM

P: 376

ok sorry, i have an anxiety problem.. thankyou very much, i will try and draw it and post it up.




#7
May709, 05:55 AM

P: 376

ok, skip on the drawing part, lol i cant draw at all, so to confirm the shape is a .... quarter of a cone, with base radius 1, and height 2?
very well explained, by the way = ) 



#8
May709, 06:14 AM

P: 376

or maybe not, because z=2y cuts through the origin and ends at (2,1,0) but a cone would have and apex at (0,0,0) instead of a cone, does it look like a pyramid with curved surface... oh i don't Im confused now




#9
May709, 07:27 AM

P: 376

ok, been thinking, i think i got it now its an upside down quarter cone, with z edges of the line z=y... therefore the apex would be at (0,0,0)




#10
May709, 07:32 AM

P: 376

no wait, coz if was a cone that would imply that z=2x aswelll.... omg i dont know, help....



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