Determine whether F is a conservative vector field. If so, find a potential function for it.
F
x
,
y
=
cos
y
+
y
cos
x
i
+
sin
x
−
x
sin
y
j
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Determine if each of the following vector fields is the gradient of a function f(x, y). If so, find all of the
functions with this gradient.
(a) (3x² + e¹0) i + (10x e¹0 - 9 siny) j
(b) (10x el0y 9 sin y) i + (3x² + e¹0y) j
a) I have placed my work and my answer on my answer sheet
2. Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such that
[₁
C₁
F. dr = 0 and
[₁
C₂
F. dr = 1
Sketch the vector field on the real line and find the stability of the fixed points.
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