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(1 point) For each of the following vector fields F, decide whether it is conservative or...


(1 point) For each of the following vector fields F, decide whether it is conservative or not by computing the appropriate fi
(1 point) For each of the following vector fields F, decide whether it is conservative or not by computing the appropriate first order partial derivatives. Type in a potential function f (that is, V f = F) with f(0,0) = 0. If it is not conservative, type N. A. F (x, y) = (-140 – 4y) i + (-4x + 12y)j f (x, y) = B. F (x, y) = -7yi - 6xj f(x,y) = C. F (2, y) = (-7 sin y)i + (-8y - 7x cos y)j f (x, y) = Note: Your answers should be either expressions of x and y (e.g. "3xy + 2y"), or the letter "N"
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A. ㅅ f(n,y) = (- 14x – 4y) î + (-42 +12y) (1) A FT +fz 心, (sa) Where fi = - 14% -47 and F2 = - An +12 y The first step is totake can with condition (3) . we lets start af zxc (n,y) ~ 144may, and then integrating constant and treat y , we get WhereB -> (1) F(x, y) = -7y î -suh A (say) fir th and fi = -ty Where -62 Fz= ir fin conservatice & first we cheek whether not . anso that ... of = f. () = (1,6) (-7 sin y siny, -8y- In cosy cosy) af = -7 siny (2) on at sy-7ncosy (3) dy with condition (2)Gwen that f(0,0) = 0 then from (7), we get c=0 f(,y) = - 7e sin (y) - 4yr

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