1056 Chapter 16 Integrals and Vector Fields EXERCISES Calculating Divergence In Exercises 1-8, find the divergence of the field. 20. Thick cylinder F D: The thick-walled c Theory and Examples 4. F sin(axy)i + cos (z)i + tan (xz)k 5. The spin field in Figure 16.13 6. The radial field in Figure 16.12 7. The gravitational field in Figure 169 and Exercise 38a in Section 163 8. The velocity field in Figure 16.14 21. a. Show that the outw xi + yj + zk thro times the volume o 1077 b. Let n be the outwa is not possible for l 22·The base of the close square in the xy-plane Calculating Flux Using the Divergence Theorem In Exercises 9-20, use the Divergence Theorem to find the outward flux of F across the boundary of the region D. x=1, y = 0, and y whose identity is unk suppose the outward f Side B is -3. Can you through the top? Give r D: The cube bounded by the planes x tly t1, and The cube cut from the first octant by the planes x = 1, y = 1, and z 1 d b a. Cube D 1078 b. Cube D: Lect13.ppt
Show transcribed image text1056 Chapter 16 Integrals and Vector Fields EXERCISES Calculating Divergence In Exercises 1-8, find the divergence of the field. 20. Thick cylinder F D: The thick-walled c Theory and Examples 4. F sin(axy)i + cos (z)i + tan (xz)k 5. The spin field in Figure 16.13 6. The radial field in Figure 16.12 7. The gravitational field in Figure 169 and Exercise 38a in Section 163 8. The velocity field in Figure 16.14 21. a. Show that the outw xi + yj + zk thro times the volume o 1077 b. Let n be the outwa is not possible for l 22·The base of the close square in the xy-plane Calculating Flux Using the Divergence Theorem In Exercises 9-20, use the Divergence Theorem to find the outward flux of F across the boundary of the region D. x=1, y = 0, and y whose identity is unk suppose the outward f Side B is -3. Can you through the top? Give r D: The cube bounded by the planes x tly t1, and The cube cut from the first octant by the planes x = 1, y = 1, and z 1 d b a. Cube D 1078 b. Cube D: Lect13.ppt
