Question

Given S is the surface of the paraboloid z= 4-x^2-y^2 and C is the curve of...

Given S is the surface of the paraboloid z= 4-x^2-y^2 and C is the curve of intersection of the paraboloid with the plane z=0. Verify stokes theorem for the field F=2zi+xj+y^2k.( you might verify it by checking both sides of the theorem)

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
In the following problems, the surface S is the part of the paraboloid z= x^2 +...
In the following problems, the surface S is the part of the paraboloid z= x^2 + y^2 which lies below the plane z= 4, and includes the circular intersection with this plane. This single surface S could also be described as being contained inside the cylinder x^2+y^2= 4. (a) Iterate, but do not evaluate, the integral ∫∫S(z+x) dS in terms of two parameters. Write the integrand in simplest form. (b) Use Stoke’s theorem to rewrite ∫S(delta X F) · ndS...
Use Stokes" Theorem to evaluate (F-dr where F(x, y, z)=(-y , x-z , 0) and the...
Use Stokes" Theorem to evaluate (F-dr where F(x, y, z)=(-y , x-z , 0) and the surface S is the part of the paraboloid : z = 4- x^2 - y^2 that lies above the xy-plane. Assume C is oriented counterclockwise when viewed from above.
Consider the part of the paraboloid x = 4 − y ^2 − z ^2 that...
Consider the part of the paraboloid x = 4 − y ^2 − z ^2 that lies in front of the plane x = 0. (a) What is its mass if its density is ρ(x, y, z) = y^2 + z ^2 g/cm^2 ? (b) What is its surface area?
Let S be the boundary of the solid bounded by the paraboloid z=x^2+y^2 and the plane...
Let S be the boundary of the solid bounded by the paraboloid z=x^2+y^2 and the plane z=16 S is the union of two surfaces. Let S1 be a portion of the plane and S2 be a portion of the paraboloid so that S=S1∪S2 Evaluate the surface integral over S1 ∬S1 z(x^2+y^2) dS= Evaluate the surface integral over S2 ∬S2 z(x^2+y^2) dS= Therefore the surface integral over S is ∬S z(x^2+y^2) dS=
Given the level surface S defined by f(x, y, z) = x − y3 − 2z2...
Given the level surface S defined by f(x, y, z) = x − y3 − 2z2 = 2 and the point P0(−4, −2, 1). Find the equation of the tangent plane to the surface S at the point P0. Find the derivative of f at P0in the direction of r(t) =< 3, 6, −2 > Find the direction and the value of the maximum rate of change greatest increase of f at P0; (d) Find the parametric equations of the...
For V = [2(x^2)y] i-( (z^3) + y) j + (3xyz) k, show that Stokes' theorem...
For V = [2(x^2)y] i-( (z^3) + y) j + (3xyz) k, show that Stokes' theorem holds by calculating both sides of the equation for a square in the x-y plane with corners at (0; 0; 0), (3; 0; 0), (3; 3; 0), (0; 3; 0) . Confirm that Stokes' theorem only depends on the boundary line by integrating over the surface of a cube with an open bottom The bounding line is the same as before.
Problem 10. Let F = <y, z − x, 0> and let S be the surface...
Problem 10. Let F = <y, z − x, 0> and let S be the surface z = 4 − x^2 − y^2 for z ≥ 0, oriented by outward-pointing normal vectors. a. Calculate curl(F). b. Calculate Z Z S curl(F) · dS directly, i.e., evaluate it as a surface integral. c. Calculate Z Z S curl(F) · dS using Stokes’ Theorem, i.e., evaluate instead the line integral I ∂S F · ds.
Compute ∫∫S F·dS for the vector field F(x,y,z) =〈0,0,x2+y2〉through the surface given by x^2+y^2+z^2= 4, z≥0...
Compute ∫∫S F·dS for the vector field F(x,y,z) =〈0,0,x2+y2〉through the surface given by x^2+y^2+z^2= 4, z≥0 with outward pointing normal. Please explain and show work. Thank you so much.
Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2 sin(z)i...
Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2 sin(z)i + y2j + xyk, S is the part of the paraboloid z = 1 − x2 − y2 that lies above the xy-plane, oriented upward.
Use Stokes' Theorem to evaluate    S curl F · dS. F(x, y, z) = x2...
Use Stokes' Theorem to evaluate    S curl F · dS. F(x, y, z) = x2 sin(z)i + y2j + xyk, S is the part of the paraboloid z = 1 − x2 − y2 that lies above the xy-plane, oriented upward.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT