Question: Let F ( x , y , z ) = ( : 0 , 0 , z: ) and S be the boundary of the

Let F(x,y,z)=(:0,0,z:) and S be the boundary of the sphere W given by x^(2)+y^(2)+z^(2)=16.
Calculate _(S)F*dS.
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
_(S)F*dS=
Calculate _(W)div(F)dV.
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
_(W)div(F)dV=
Let F ( x , y , z ) = ( : 0 , 0 , z: ) and S be

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

Section 4.1: (page 247) Numbers 1, 3, 7-13 odd, 19-23 odd Section 4.2: (page 260) Numbers 1, 5, 13, 19a, 20a Section 4.3: (page 270) Numbers 1-5 odd textbroker.com X Final Exam X X Canvas LMS X...

Q:

Let C2 be the oriented curve parametriza r(t)= cost V2 ,sint, - cost V2 ), Osts2 n. Let F( x, y, z) = , and let I2=_ F-dr. [Suggestion: Use Stokes' Theorem and the fact that C 2 is the circle in the...

Q:

solve the answers handwritten but please type all the final answers together in the different section after solving. Thanks. 1. [-/1 Points] DETAILS SCALCET9 14.1.004. Let h(x, y) = e (a) Evaluate...

Q:

textbroker.com X Final Exam Canvas LMS X MATH140-12141 (ONL) X BusCalc.pdf X *Dashboard X C D File | /Users/davidorozco/Downloads/MathG140FinalExam-Summer2023%20(1).pdf Update : Suggested Sites M...

Q:

Let S be the surface in R defined by f x y z 0 The tangent plane of S at 2 9 1 is defined by 7 x 2 9 y 9 z 1 0 a Given the equation of the tangent plane to S enter in the box below a column vector v...

Q:

Question 7 [10 Marks] Let C be the curve of intersection of the cylinder x2 + (y 1)2 = 1 with the plane y = z, traversed in the counterclockwise direction when viewed from the above. Let F (x, y, z)...

Q:

1. In Topic 4.2 (The Definite Integral II), we considered f(x)=19-x on [-3, 3] We know that the function produces a semi-circle and the definite integral gives the area between the curve and the...

Q:

Please provide neat and clean solution A function is given f : R3 + 12 f(z, y, 2 ) = (242+2) - (10) let the equation f (x, y, z) = (0, 0) in the Point (x0, yo, 20) = (3, 4, 2) . locally unique H a)...

Q:

Problem 3 (14 points) Let f (x, y, z ) = 3 x2 +y2+ 2 2 , if (x, y, z) # (0, 0, 0) 0. if (x, y, z) = (0, 0, 0) (a) Use the definition to find the directional derivative of the function f at (0, 0, 0)...

Q:

Given a vector-valued function f: Rd R, the gradient or the gradient matrix of f, denoted by Vf, is the d x k matrix - (+48) Vf Vf2 Vf Let f (x, y, z) af ????1 How many columns does Vf (x, y, z)...

Q:

Reconsider the model given in Prob. 7.3-1. While doing sensitivity analysis, you learn that the estimates of the right-hand sides of the two functional constraints are accurate only to within 50...

Q:

Peninsula Tour Company is located in a tourist town on Georgian Bay. The small town is quiet during the winter months but comes alive with tourists from May to October. The company is planning for...

Q:

2 A student investigates the movement of a suspended metre rule. Metre rule A is clamped horizontally above the bench, as shown in Fig. 1.1. (a) Describe how the student checks that A is horizontal....

Q:

What are some food related health care issues that inner cities are more likely to see than more affluent areas? Why are certain areas most likely to experience inadequate healthy food options than...