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Unformatted text preview: a maximum. 6. (10 Points) Section 3.4, Exercise 2 Find the extrema of f ( x,y ) = xy subject to the constraint x 2y 2 = 2 . 7. (10 Points) Section 3.4, Exercise 20 A light ray travels from point A to point B crossing a boundary between two media ( see Figure 3.4.7 of the text ) . In the ﬁrst medium its speed is v 1 and in the second v 2 . Show that the trip is made in minimum time when Snell’s law holds: sin θ 1 sin θ 2 = v 1 v 2 . 2 8. (10 Points) Section 3.4, Exercise 22 Let P be a point on a surface S in R 3 deﬁned by the equation f ( x,y,z ) = 1 , where f is of class C 1 . Suppose that P is a point where the distance from the origin to S is maximized. Show that the vector emanating from the origin and ending at P is perpendicular to S ....
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 Spring '08
 Ramakrishnan
 Math, Calculus, Linear Algebra, Algebra, Continuous function, 2W

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