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Question

Sketch a typical level surface for the function. ƒ(x, y, z) = z

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Answered 1 year ago
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To obtain a level curve for f(x,y,z)=z, replace f(x,y,z) with constant c\text{To obtain a level curve for $f(x,y,z)=z$, replace $f(x,y,z)$ with constant $c$. }

c=zc=z

The above equation represents a plane which is perpendicular to the zz-axis and parallel to both the xx and yy axes.

The graph below shows the level curves corresponding to c=1,2,3c=1,2,3

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