A vortex that rotates at constant angular velocity w about the z-axis has velocity vector field = w(-yi+xj). (a) Sketch, on a separate sheet of paper, the vector field with w= 1 and the vector field with w=-1. Then determine the speed of the vortex as a function of the distance from its center, r. speed = (b) Compute div and curl . div = curl = (c) Compute the circulation of counterclockwise about the circle of radius R in the zy-plane, centered at the origin. circulation =

Q: 6. A B.

A: We have to find y

Q: ds 5. I135+1 6. IT x² +1 dx

A:

Q: y³y −3= ... Oa. 1/y Ob.y O C. 1 c. Od.0

A: Given expression isy³.y-3

Q: Evaluate. 4 10x + 1 dx 5x2 + x %3D

A: This is the definite integral, firstly integral will be calculated after that limit will put

Q: :2 ¡dx 4

A:

Q: Ofind dy fort-

A:

Q: 12. Find DC 3. 10 D

A: We need to find DC.

Q: 6x dx. Jo 1+x2 9. Evaluate

A:

Q: 2 6² 6² S (3x + 4y) 5dxdy 0 Find

A: We need to evaluate :

Q: 3x? dx 2 + 4x

A:

Q: C 3 %3D BA = %3D

A:

Q: d. Se-7x+10 dx

A: We have to evaluate the integral.

Q: Solving a System of Linear

A:

Q: 2. Evaluate 6x²e4x³ dx.

A: Let 4x3 = t

Q: Evaluate. 6. 2 4x 4 dx

A:

Q: 3. %3D 3170

A: First convert mixed fractions to improper fractions

Q: Find the value of sec '(0.5) O a. -7/2 Ob. O b. T O. undefined 1/4

A: