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(1) The paraboloid z = 9 − x − x2 − 7y2 intersects the plane x...

(1) The paraboloid z = 9 − x − x2 − 7y2 intersects the plane x = 1 in a parabola. Find parametric equations in terms of t for the tangent line to this parabola at the point (1, 2, −21). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)

(2)Find the first partial derivatives of the function. (Sn = x1 + 2x2 + ... + nxn; i = 1, ..., n. Give your answer only in terms of Sn and i.)

u = sin(x1 + 2x2 + ⋯ + nxn)

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