Sketch a typical level surface for the function.
-$$f ( x , y , z ) = e ^ { \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) }$$

Question

Quizplus · Accepted Answer

The level surfaces of the given function are of the form $e^{x^2+y^2+z^2}=k$, where $k$ is a constant. Taking logarithm on both sides, we get $x^2+y^2+z^2=\log k$. This represents a sphere with center at the origin and radius $\sqrt{\log k}$. Therefore, the level surfaces are spheres of increasing radii as we move away from the origin. Option A depicts such a surface.

Sketch a Typical Level Surface for the Function f(x,y,z)=e(x2+y2+z2)f ( x , y , z ) = e ^ { \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) }f(x,y,z)=e(x2+y2+z2)

Sketch a Typical Level Surface for the Function $f ( x , y , z ) = e ^ { \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) }$