1. A function y = f(x,2) is defined by letting f(x, 2) = 1 – x² – (z – x)². Let S be the surface defined by S = {{x, y, z) : y = f(x, 2)}. So S is a skewed paraboloid that opens downward. Suppose (ro, yo, 2o) is a point lying on S. Give a formula for a normal vector n = n(xo, Yo, 2o) which is normal (perpendicular) to S at (ro, Yo, žo). It not required that n be a unit vector, but it should point upward (with y component positive).

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A:

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