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) = (2x + 5y)i + (5x + 4y) j f (x, y) = B. F(x, y) = yi + 2xj f (x, y) = N C. F(x, y) = (sin y)i + (10y + x 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"
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) = (2x + 5y)i + (5x + 4y) j f (x, y) = B. F(x, y) = yi + 2xj f (x, y) = N C. F(x, y) = (sin y)i + (10y + x 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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Transcribed Image Text: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, Vf = F) with
f(0, 0) = 0. If it is not conservative, type N.
A. F(x, y) = (2x + 5y) i + (5x + 4y) j
f (x, y)
=
B. F(x, y) = yi + 2xj
f (x, y)
= N
C. F (x, y) = (sin y) i + (10y + x 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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