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hmwk8 - (HINT This is done on pages 1093–1094 17.4b Note...

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Math 215 Homework Set 8: §§ 17.3 – 17.4 Winter 2008 Most of the following problems are modified versions of the recommended homework problems from your text book Multivariable Calculus by James Stewart. 17.3b. Let F = ± f where f ( x, y ) = sin(2 y - x ) . Find curves C 1 and C 2 that are not closed and which satisfy the equations ± C 1 F · d r = 0 ± C 2 F · d r = 1 . 17.3c. Do Problem 11 of § 17.3 in Stewart’s Multivariable Calculus . 17.4a. Use Green’s theorem to show that if D is a region bounded by a simple closed curve C , then the area of D is given by the formulas ² C x dy, ² C y dx, or 1 / 2[ ² x dy - y dx
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Unformatted text preview: ] . (HINT: This is done on pages 1093–1094.) 17.4b. Note that if C is the line segment connecting the point ( a, b ) to the point ( c, d ) then, ± C x dy-y dx = ad-bc. Show (using Green’s theorem) that if ( a, b ) , ( c, d ) , and ( e, f ) are the vertices of a triangle, then the area of the triangle is given by the formula 1 / 2[( ad-cb ) + ( cf-ed ) + ( eb-af )] . 17.4c. Generalize the above problem by doing Problem 21 of § 17.4 in Stewart’s Multivariable Calculus ....
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