exam3-takehome

# exam3-takehome - Math 223-008 Exam 3 Take Home Part Due on...

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Math 223-008 Exam # 3 – Take Home Part Due on Monday 4 April 2005 at the beginning of class. Partial credit is possible, but you must show all work. Name: I hereby testify that this is individual work. Signed: 5. Consider the vector field -→ F = y - 1 x 2 + ( y - 1) 2 -→ i - x x 2 + ( y - 1) 2 -→ j (a) Show that -→ F is a conservative vector field. (b) Justify why Green’s theorem cannot be applied to find contintegraltext C -→ F · d -→ r for the curve C described below (and traced in the counterclockwise direction). (Hint: Where is the singularity?)

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2 -1 -0.5 0.5 1 0.5 1 1.5 2 (c) Find the integral contintegraltext C -→ F · d -→ r by constructing a reasonable curve that would simplify your work tremendously. Parametrize your “reasonable curve” then calculate the line integral. The alternative is to use the following parametriza-

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