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Consider the function F(x, y, z) =x2/2− y3/3 + z6/6 − 1. (a) Find the gradient...

Consider the function F(x, y, z) =x2/2− y3/3 + z6/6 − 1.

(a) Find the gradient vector ∇F.

(b) Find a scalar equation and a vector parametric form for the tangent plane to the surface F(x, y, z) = 0 at the point (1, −1, 1).

(c) Let x = s + t, y = st and z = et^2 . Use the multivariable chain rule to find ∂F/∂s . Write your answer in terms of s and t.

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