Describe and sketch the level surfaces of the functions
a) (,,)= √++ and b) (,,)= − −
The value of is the distance from the origin to the point in 3-dim space (, , ). Each
level surface √++ = > is a sphere of radius centred at the origin. What are coordinates of origin? Describe the level curves in the − plane and in the − plane. Sketch a typical level surface for the function.
The level surfaces of constant = will be different for = , > and < . Read back through notes to see in which cases the surfaces are cones or hyperboloids
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