Solve the problem.
-Find an equation for the level surface of the function $f ( x , y , z ) = x + e y ^ { + } z$ that passes through the point $( 9 , \ln ( 2 ) , \ln ( 9 ) )$.
A) $\ln ( x ) + y + z = 27$
B) $x + e ^ { y + z } = 27$
C) $x + \mathrm { e } ^ { + } \mathrm { z } = 20$
D) $x + e ^ { y + z } = 18$

Question

Quizplus · Accepted Answer

A level surface of a function is a surface in 3D space where the function has a constant value. We want to find the equation of the level surface of the function $f(x,y,z) = x + ey + z$ that passes through the point $(9,\ln(2),\ln(9))$. This means that we want to find values of $x$, $y$, and $z$ such that $f(x,y,z) = k$ where $k$ is the constant value of the level surface passing through the given point. So we have:
$$f(x,y,z) = x+ey+z = k$$
$$9 + e^{\ln(2)} + \ln(9) = k$$
$$k = 18$$
So the equation of the level surface passing through the point $(9,\ln(2),\ln(9))$ is:
$$x + e^{y+z} = 18$$
which is choice (B).

Solve the Problem f(x,y,z)=x+ey+zf ( x , y , z ) = x + e y ^ { + } zf(x,y,z)=x+ey+z

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