Compute the flux of the vector field F = 9x²y² zk through the surface S which is the cone √√x² + y² = z, with 0 ≤ z < R, oriented downward. (a) Parameterize the cone using cylindrical coordinates (write as theta). x(r, 0) = y(r, 0) = z(r, 0) = with and

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

A:

Q: Find the directional derative of f at the point P0(1,1) in the direction of the vector A = 3i - 2j…

A: Direction derivatives at (1,1) is given in direction of A = 3i - 2j.

Q: Find a vector-valued function r(t), that represents the following curve. Be sure to include an…

A: The vector valued functions in the parametric form can be represented as:…

Q: Consider the space curve C given by the vector function f(t) = (t² + 1)i + (2t4 – 3t2)j +t³k where t…

A:

Q: -y+25 Let F (x, y, z) := x+yz7 3+2⁹ let n be the outward unit normal vector. Evaluate Sf (curl F) ·…

A:

Q: Find a vector valued function which gives the curve of intersection of  y2 + z2 =16  with the plane…

A: Given the curves:

Q: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

A:

Q: Sketch (a) the level surfaces of the scalar point function f(r) = ze; (b) the field lines of the…

A: Given Information:a) Scalar point function: f(r)=ze−xyb) Vector point function: F→(r)=(−y,x,1)To…

Q: Find a formula F = (F₁(x, y), F₂(x, y)) for the vector field in the plane that has the properties…

A: Answer :

Q: The normal vector to the tangent plane for the surface x²y³ z = 8, at the point (-1, 2, 1) is: 2 3…

A:

Q: Let S be the surface obtained by revolving the plane curve 2x=sqrt(9−y2) about the y-axis.Obtain a…

A: Given- Let S be the surface obtained by revolving the plane curve 2x = 9 - y2 about the y-axis. To…

Q: Compute the flux of the vector field F = : 4xi + 4yj through the surface S, which is the part of the…

A:

Q: Q1.

A:

Q: Find the flux of the vector field F(x, y, z) =(x)i+(y)j+(z)k through the surface S of the…

A:

Q: y Consider the surface of equation z = X+Y² What is the equation for the tangent line to S at the…

A: This is a problem of vector calculus.

Q: A force field (in newtons) is defined by F(x, y) = [ + + x, 1 x² +1 y³ зав where coordinates x and y…

A:

Q: Suppose F(x, y) = x² + y²j and C is the line segment segment from point P = (-3,-4) to Q = (-3, 1).…

A:

Q: Compute the integral of ſA° · dľ°P2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector function…

A: We have to find the integral from point p1 TP p2.

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

A:

Q: 6. (a) Show that the curve represented by the vector function F(t) = (5t, 3t – 4, 2t² – 6) is at the…

A:

Q: F(x,y,z) = ⟨1,y,z^4/3⟩ a. Find the parametric equation of a curve passing through the point…

A: Consider the given vector field. F(x,y,z)=1,y,z43 and  a curve passing through the point ro=-1,1,1…