#5 with all the steps in a clear way please!! In Exercises 3-10, compute the curl...
For each of the following vector fields, find its curl and
determine if it is a gradient field.
(1 point) For each of the following vector fields, find its curl and determine if it is a gradient field. (a) F = 5(xy + 22) + 10(x2 + y2) 7+ 10(x2 + y2) k. curl F = F ? (b) Ğ = 5yzi + (52z+z2) 7+ (5xy + 2yz) k: curl Ĝ = Ğ ? (c) H = (5xy + yz)...
#7, #11, #17 please
Calculating the Curl and the Divergence In Exercises 1-20, calculate curl F and divF of the given vector fields F. F = 1 1. F= (°yz?, xyz, wy) 2. F= (x+y23, xyz2, xz) 3. F= (zey, well, ye**) 4. F = (xeyz, zety, ye** ) 5. F= (xsin yz, y sin xz, zsin zy) 6. F = (y sin uz, e sinyz, 2 sinxy) 7, F = (sin x cos z, sin y cos x, sin...
Solve with all the steps please!
Calculate the divergence and the curl of the vector field F(x,y,z) = ( x^3y)i + (xy)j + ( 213 )k. (Where Fis a vector and i,j,k stand for the standard unit vectors)
Help. Cant figure this one out. I keep messing up somewhere. please
sent full steps. THANKS IN ADVANCE. I will thumbs up!
13. For the vector field F(x, y, z) = (xy + yºz)i + (y2 + x2 +e+2) 3 + (zz - sin(xy) + y2), compute the divergence of Ě, i.e. compute div = 7. F. Then, using the divergence theorem, compute the surface integral (fux across S) ST. P. 25, where S is the outward- oriented, closed surface...
NO.25 in 16.7 and NO.12 in
16.9 please.
For the vector fied than the vecto and outgoing arrows. Her can use the formula for F to confirm t n rigtppors that the veciors that end near P, are shorter rs that start near p, İhus the net aow is outward near Pi, so div F(P) > 0 Pi is a source. Near Pa, on the other hand, the incoming arrows are longer than the e the net flow is inward,...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
Please show all steps, even the steps that seem like common
sense.
0/3 POINTS PREVIOUS ANSWERS SCALCET8 16.7.031. 7/20 Submissions Used Evaluate the surface integral // F.ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. Is F(x, y, z) = x2 i + y2 j + z2k S is the boundary of the solid half-cylinder o SzSV 9-y2,0 SX...
please answer all qustion on expination needed
1 Find a vector of magnitude 3 in the direction of v=5 i - 12 k The vector is i+i+k (Simplify your answer. Use integers or fractions for any numbers in the expression) 2 Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations x2 + y2 +(2+152 = 169, z= - 3 Choose the correct description O A. The line through (5,0. -...