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6-given-x-2-3-x-y-2-y-z-y-2-z-2-11-0-is-an-implicit-function-pa767

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6. Given \( x^{2}+3 x y+2 y z+y^{2}-z^{2}-11=0 \), is an implicit function \( z=f(x, y) \) defined around the point \( (x=1, y=2, z=0) \) ? If so, find \( \partial z / \partial x \) and \( \partial z / \partial y \) by the implicitfunction rule, and evaluate them at that point.