Verify Stokes' Theorem for the given vector field and surface, oriented with an upward - pointing normal. F = (:yz, 0,x:), the portion of the plane where x,y,z ≥ 0 +~+z = 1, X y 2 3

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: 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: Given w f(z,y, 2) = zy²z. Find: Ograd/(1,3,-2) 3. (b) equation of the tangent plane to the surface…

A:

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: Calculate the directional derivatives of the function x²y x²+ y? for (x, y) +0 f(x,y) = for (x, y)…

A:

Q: (b) Given that a is the surface of the solid G enclosed by cone 2-4-√√². and plane z -0. (1) Compute…

A:

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

A:

Q: 6. Use the Normal Vector to a Smooth Parametric Surface to find the equation of the tangent plane to…

A:

Q: Let the temperature / in degrees at the point X,y,z), with distances measured in cm, be T(X,y,z)=5x…

A:

Q: Let C be a curve defined by some vector function R with unit binormal B such that R(0) = (-2, 5, 4)…

A: Given C1 is a curve defined by some vector function R→ with unit binormal B→ such that R→(0)=-2,5,4,…

Q: Let S be the surface described by the vector function Ř(u, v) = (v², u + v, e²«). Find an equation…

A:

Q: For the vector function: r(1)=(Sf,21,5). find %3D (a) r'(t) and r'(4) vileuponi od yd bolbni PA pe…

A: The derivative of a vector function is obtained by differentiating all the components of that…

Q: Identify the surface by eliminating the parameters from the vector-value r(u.v) = 3 cosv cosui +3…

A:

Q: Sketch the curve with the given vector equation by finding the following points. r(t) = (2, t, 4-t²)…

A:

Q: Given the vector function: 7(t) = (e', e' sin(t), e cos (t)) Determine the equations of the normal…

A: