Question

Suppose you need to know an equation of the tangent plane to a surface S at the point P(3, 1, 4). You don't have an equation for S but you know that the curves r1()(3 2t, 1 - t2,4 5t+t2) r2(u) (2u2, 2u3 1, 2u 2) both lie on S. Find an equation of the tangent plane at P. Find an equation of the tangent plane to the given surface at the specified point. = 4x2y2-9y, (1, 4, 16) z

Answer 1

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lane Theulae the Hatien C30, 14, 12<3, y-1,- o 30(1-7)-19 19-1)4 1s ( 2-4) (2t- Y 301- 40-141 1 301-149 12 2 124 G2 2 -4 Civen - 91 -2 Flus, (,41-14) 3-9--1 Eapati an of tad lone Mo Jo f Cordrt)t) 0

(x-)-13-1) - I l2 4 16) - 0 -j-t - 26O 1-2 8-16