Let G be a solid whose surface σ is oriented outward by the unit normal n, and let F x , y , z denote a vector field whose component functions have continuous first partial derivatives on some open set containing G . The Divergence Theorem states that the surface integral ___________ and the triple integral ___________ have the same value.
Let G be a solid whose surface σ is oriented outward by the unit normal n, and let F x , y , z denote a vector field whose component functions have continuous first partial derivatives on some open set containing G . The Divergence Theorem states that the surface integral ___________ and the triple integral ___________ have the same value.
Let G be a solid whose surface
σ
is oriented outward by the unit normal n, and let
F
x
,
y
,
z
denote a vector field whose component functions have continuous first partial derivatives on some open set containing G. The Divergence Theorem states that the surface integral
___________
and the triple integral
___________
have the same value.
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.
A vector field F = x(x² – y²) + ŷ(2xy + y?)
a) f d.č =? c on the closed curve in the figure
b) S(7xF). dà =?
c) Can F be written as the gradient of a scalar?
2.
(Note: There may be deficiencies in the question and you
can solve it by making the necessary changes.)
2.
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
Precalculus: Mathematics for Calculus - 6th Edition
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