How many variables are used to parameterize a surface in R^3? What kind of geometric object is the boundary of a surface? How many variables are used to parameterize the boundary of a surface? Find a parametric representation for the upper half, Z ≥ 0, of the surface 2x^2 + 3y^2 + z^2 = 6.

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in R^{3} the abjects are of 3 D.form\Rightarrow The a bject having length, breadth and height as well.in othso word the abject having cross section in ane of plare.So in 3 D \rightarrow ingenerd we haue two Parametor paramatrization.at toundory of surface oell Pain's are of R^{3}. So it also has 2 two variable.To find the parametrization af z \geqslant 0 and 2 x^{2}+3 y^{2}+z^{2}=6\begin{array}{l}z^{2}=6-2 x^{2}-3 y^{2} \\z=\sqrt{6-2 x^{2}-3 y^{2}}\end{array}\begin{aligned}R(x, y)= & \left(x, y, \sqrt{6-2 x^{2}-3 y^{2}}\right) \\& -\sqrt{3} \leq x \leq \sqrt{3} \\& -\sqrt{2} \leq y \leq \sqrt{2}\end{aligned} ...