MAT235Y1 Lecture Notes - Lecture 1: If And Only If, Farad, Closed Set

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30 Jul 2018
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MAT235Y1 Full Course Notes
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Solution i : (partial): use the formula for distance p of p from the plane. We have a plane x + 2y + z = 4 and p(1, 0, -2). F(x, y) local vs global/absolute extremum (min/max) points. If fx and fy exit, then local extreme points are critical points, (cid:1487)(cid:1858)(cid:4666)(cid:1876),(cid:1877)(cid:4667)=(cid:882) . Classification of critical points is done by the second derivative test. Find the closest point to p on the plane and its distance from p. p. Min d(x, y) = ? the surface z = 4 x 2y. Solution ii: (full) the distance of p from a general (x, y, z) (cid:1488)(cid:2870) (cid:1871) (cid:4666)(cid:1876) (cid:883)(cid:4667)(cid:2870)+(cid:1877)(cid:2870)+(cid:4666)(cid:1878)+(cid:884)(cid:4667)(cid:2870) on. The distance of a point on the surface from p is. If min d(x, y) is attained at (cid:4666)(cid:1876)(cid:2868),(cid:1877)(cid:2868)(cid:4667), then also the min f(x, y) = d2(x, y) is (cid:1858)(cid:4666)(cid:1876),(cid:1877)(cid:4667)=(cid:4666)(cid:1876) (cid:883)(cid:4667)(cid:2870)+(cid:1877)(cid:2870)+(cid:4666)6 (cid:1876) (cid:884)(cid:1877)(cid:4667)(cid:2870) (cid:4666)(cid:1876)(cid:2868),(cid:1877)(cid:2868)(cid:4667) s. t. f(cid:4666)(cid:1876)(cid:2868),(cid:1877)(cid:2868)(cid:4667) = min f(x, y)

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