Consider the surface S consisting of the portion of the graph of the function z = x2 + y? above the annulus 4

Q: The vector equation r (u, v) = = u cos vi+usin vj + vk, 0 ≤ v ≤ 10m, 0 ≤ u ≤ 1, describes a helicoid…

A:

Q: Evaluate F. dS , where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 1, 0 < v<T…

A: since, y,-x,z3 and, ru,v=u cosv, u sinv,v So, F⇀ru,v=u cosv,-u sinv, v3 Now the normal upward vector…

Q: Your friends correctly calculate the gradient vector for f(x, y)=x²+y at the point (2,-3) as…

A:

Q: Give a scalar equation for a plane at distance 9 from the plane P with equation 2x+y+2 = 4 0=0

A:

Q: Let f(x, y) = x^2/(x + y). Find a unit vector u such that Duf(1, 2) = 0

A: f(x, y) = x^2/(x + y)

Q: g(x,y,z)=x^2+y^2+(z-3)^2

A: For (a), We need to find the equation of the tangent plane to the level set g(x, y, z) = c at the…

Q: If the given three vectors are coplanar, then find the value of x. A = i-2j + 3k, B = xj + 3k, C =…

A: A, B, C are coplanar.So

Q: 3. Consider the parametric vector equation of a cone r(u, v) = u cos vi + u sin vj + uk with 1<u < 2…

A: The volume  of a cone with radius r  and height  h is given by  V=13πr2h.   Given a  function…

Q: Use Stokes' Theorem to find the circulation of F= 2yi +423 +3ack around the triangle obtained by…

A:

Q: Verify the Divergence Theorem for F = (-2, 3, 2³) across the surface of a sphere of radius 4 with…

A: