Methods 2 Notes 3

Question 1

(3R-N63-) Equations 3.1.3 - 3.15. How they are derived. FTC in one variable only we have arrive at the relation…w intergrand partial d f / partial d y for first one. Basically derive green’s theorem.

Answer 1

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Question 2

(3T-N64-) Green’s Thoerem

Answer 2

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Question 3

(3T-N64-) Divergence theorem

Answer 3

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Question 4

(3E-N66-3.1) Verify Green’s Theorem for F = (x^2- y)i + (y^2 + x)j if C is the circle (x -3)^2 + (y-3)^2 = 1 in the xy-plane oriented anti-clockwise.

Answer 4

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Question 5

(3E-N67-3.2) Let F = sin(x)i + (x + y)j. Let’s find the line integral of F around the perimeter of the rectangle with corners (3, 0), (3, 5), (1, 5), and (1, 0), traversed in that order. If we want to use Green’s Theorem, we need to make certain that it’s applicable.

Answer 5

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Question 6

(3E-N67-3.3) F = xj and consider any closed curve C in the plane. Work out integral

Answer 6

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Question 7

(3E-N67-3.4) The ellipse given by x^2/a^2 + y^2/b^2 = 1 is parameterized by r(t) = a cos(t)i + b sin(t)j with 0 <=t

Answer 7

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