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Numerade Educator

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Problem 44 Medium Difficulty

Sketch the region bounded by the paraboloids $ z = x^2 + y^2 $ and $ z = 2 - x^2 - y^2 $.

Answer

The region is inside the intersection of the two paraboloids in the middle of
the graph.

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Video Transcript

So here in this question we have to sketch the parable lights Which is z equals two x square. Bless the white square and Is he equals 2? Two minus x squared minus y square. Now I'm going to plot this parable Lloyd 1st on this graph paper. Now it looks like this, it will be an upward para polaroid like this and it will pass from Z equals to zero, this is equal to zero. And here this is one, this is two. The next one, this is two minus X squared minus y squared. Now this would be a downward parabola Lloyd And it will pass from z equals to two like this. No, the region that we need to sketch is this region. This is basically this would be a 3D region. So this is the solution that was asking the question. I hope it was a problem. Thank you.