I have to find surface area of set $M=\left\{(x,y,z): e^x+e^{-x}=z-\sqrt3y, 0<y<x<1\right\}$ and my problem is to parametrize it, may you help me?
2026-03-28 13:21:21.1774704081
How to find a parametrization of the set $\left\{(x,y,z): e^x+e^{-x}=z-\sqrt3y, 0<y<x<1\right\}$?
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Just pick as a parametrization
\begin{equation} \phi(x,y) : (0,1)\text{ x }(0,1)\to\mathbb R^3 : (x,y)\mapsto (x,y,e^x+e^{-x}+\sqrt3y) \end{equation}
You just use the domain given in the definition and set z as in the equation you have above. :)