Question

there is first question E then there is the question of the value of the line integral ,then quwstion A, then question 1, and the last two pictures are one question

Question E (5 points) By Green's theorem, the value of the line integral y 4 is: , where C is the curve given by a) 3 c) 12t d) 27T e) If none of the above is correct, write your answer here in a box rover the line segment from (0,-2) to (4.0) The value of the line integral of 5 In 2 b) 5 In3 d) e) If none of the above is correct, write your answer here in a box: Question A Then Let a)) 0)-0 b be exten 11)-0 t,)can be extended to become continuous at (1,1) by defining ,can be extended to become continuous at (1,1) by defining c) can be extended to become continuous at (1,1) by defini/ d))cannot be extended in any way to make it continuous at (1,1). Question (y' - y)dx + (2xy-2y)dy Apply Green's theorem to evaluate C , where C is the boundary of the region in the first quadrant enclosed by the x-axis, the line a) 1 b) -1 c) 2 d) -2 sin x and the curve 4) (10 points) Consider the field (x,y,z)- yz+ 1t x a) (7 points) Show that F is conservative and find a potential function for F (3 points) Use the Fundamental Theorem of Line Integrals to evaluate the work done by F from A(0,1.2) to B(12,e) y)_+ (x +y)/and the circle C: (10 points) Consider the vector field F xy)-(x xoriented counterclockwise Verify Gireen's Theorem by calculating the around C using a line integral then using a double integral. circulation of

Answer 1

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