Circulation and flux For the following vector fields, compute (a) the circulation on and (b) the outward flux across the boundary of the given region, Assume boundary curves have counterclockwise orientation. 41. F = ∇ ( x 2 + y 2 ) , where R is the half annulus { ( r , θ ) : 1 ≤ r ≤ 3 , 0 ≤ θ ≤ π }
Circulation and flux For the following vector fields, compute (a) the circulation on and (b) the outward flux across the boundary of the given region, Assume boundary curves have counterclockwise orientation. 41. F = ∇ ( x 2 + y 2 ) , where R is the half annulus { ( r , θ ) : 1 ≤ r ≤ 3 , 0 ≤ θ ≤ π }
Circulation and fluxFor the following vector fields, compute (a) the circulation on and (b) the outward flux across the boundary of the given region, Assume boundary curves have counterclockwise orientation.
41.
F
=
∇
(
x
2
+
y
2
)
, where R is the half annulus
{
(
r
,
θ
)
:
1
≤
r
≤
3
,
0
≤
θ
≤
π
}
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.
Let f be a function whose graph consists of 5 line segments and a semicircle as shown in the figure below.
Let g(x) = √ƒƒ(t) dt .
0
3
2
-2
2
4
5
6
7
8
9
10
11
12
13
14
15
1. g(0) =
2. g(2) =
3. g(4) =
4. g(6) =
5. g'(3) =
6. g'(13)=
The expression 3 | (3+1/+1)
of the following integrals?
A
Ов
E
+
+
+ +
18
3+1+1
3++1
3++1
(A) √2×14 dx
x+1
(C) 1½-½√ √ ² ( 14 ) d x
(B) √31dx
(D) So 3+x
-dx
is a Riemann sum approximation of which
5
(E) 1½√√3dx
2x+1
2. Suppose the population of Wakanda t years after 2000 is given by the equation
f(t) = 45000(1.006). If this trend continues, in what year will the population reach 50,000
people? Show all your work, round your answer to two decimal places, and include units. (4
points)
Chapter 14 Solutions
Student Solutions Manual, Single Variable for Calculus: Early Transcendentals
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