Assume C is a circle centered at the origin, oriented counter clockwise, that encloses disk R in the plane. Complete the following steps for each vector field F. a. Calculate the two-dimensional curl of F . b. Calculate the two-dimensional divergence of F. C. Is F irrotational on R ? d. Is F source free on R ? 13. F = 〈 4 x 2 y , x y 2 + x 4 〉
Assume C is a circle centered at the origin, oriented counter clockwise, that encloses disk R in the plane. Complete the following steps for each vector field F. a. Calculate the two-dimensional curl of F . b. Calculate the two-dimensional divergence of F. C. Is F irrotational on R ? d. Is F source free on R ? 13. F = 〈 4 x 2 y , x y 2 + x 4 〉
Solution Summary: The author calculates the two dimensional curl of the vector field F=langle x,yrangle with f(x.y)=4x3y and
Assume C is a circle centered at the origin, oriented counter clockwise, that encloses disk R in the plane. Complete the following steps for each vector field F.
a. Calculate the two-dimensional curl of F.
b. Calculate the two-dimensional divergence of F.
C. Is F irrotational on R?
d. Is F source free on R?
13. F =
〈
4
x
2
y
,
x
y
2
+
x
4
〉
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.
2. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.4.006.MI.
Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
7y2
y²
11
dy
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3. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.4.009.
Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
tan³(12/z) dz
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4. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.4.014.
Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.)
5 sinб12x dx
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