Problem #10: Find the flux of F(x, y, z) = yi — xj + 7k across S, where S is the helicoid with vector equation r(u, v) (u cos v, u sin v, v), 0 ≤ u ≤ 1, 0 ≤ v ≤ 6. =

Q: Define two vector functions F(t) = 8 sin(t)i + 6 cos(t)j + (t – 2)k ü(t) = 6 sin(t)i + 8cos(t)j + (t…

A: We have to find the dot product of r(t) and u(t)

Q: Question 2. Prove that ₹n³ + n³ +n is an integer for every integer n.

A: 2.  To prove that is an integer for every integer n.

Q: ordinary deck of 52 cards various five-card holdings are given special names. The name "two pairs"…

A: Detailed explanation mentioned below

Q: Q1/ If f(x,y)=find a unit vector u for which Duf (2,3) = 0 x+y

A: We have to find a unit vector u for which Duf(2,3)=0 where f(x,y)=yx+y

Q: If r(t) = u(t) x v(t), where u and v are the vector functions given below, find r'(2). u(2) = (6, 3,…

A: To find r'(2).

Q: C

A:

Q: Define two vector functions 7(t) = 2 sin(t)i + 8 cos(t)j + t°k ü(t) = 8 sin(t)? + 2 cos(t)j + (t? –…

A:

Q: Suppose f(x, y) = sin( (a) Vf(x, y) = = (b) Vƒ(3, π) = 2y x T 2y 2y 2y cos cos 2) Con (2) 200m (20 -…

A: Given that , fx,y=sin2yx and u is the unit vector in the direction of 1,1.

Q: True or False: Given a function of two variables f(x, y), the vector Vf(a, b) is perpendicular to…

A: It is false. The gradient vector ∇fa,b is not perpendicular to the graph z=fx, y at the point with…

Q: (4) Find the gradient vector Vf(z,y) of the function f(z,y) = 3x²y.

A:

Q: 2y X in the direction of (1, 2). Then, Suppose f(x, y) (a) ▼ f(x, y) = (b) ▼ ƒ(6, π) = = = sin (c)…

A:

Q: Let f(x,y,z) = x2 y−xy2+z3, P(1,1,2), u is the vector from P to Q(1, −2, −2). Determine the maximum…

A:

Q: Let f(x, y, z) = x²y - xy² + z³, P(1,1,2), u is the vector from P to Q(1, -2,-2). Determine the…

A: The given problem is to determine the maximum and minimum directional derivative of the given…

Q: Let the temperature T in degrees at the point (x,y,z), with distances measured in cm, be T(x,y,z)=3x…

A: Here I am attaching image so that you understand each and every step.

Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A: The given potential function is Vx,y,z=2x2-5xy+xyz. (a) To Find: Rate of change of the function at…

Q: You are given the derivative of a vector function r in the component form is dr (e,3e",-2t). You are…

A: Given that: drdt=<e-t, 3e3t, -2t>          and r(0)=2i-j+k

Q: 5. Compute the directional derivative and gradient of f(x, y, z) = 4x – y²e3xz at (2, – 1, 0) in the…

A: Gradient of vector function For a given vector f(x, y, z) the gradient vector denoted by ∇(f) is […

Q: The acceleration of a particle at any time >=0 is given by: dr a = == (25cos2t)i + (16sen2t)j +…

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: Find Duf at (2,−1,1) for f(x, y, z) = 3x5y²z³ in the direction given by u = (1/3, 2/3, −2/3).

A: Given function:- fx,y,z=3x5y2z3

Q: Compute the directional derivatives of the following functions along unit vectors at the indicated…

A:

Q: 5. For f(x, y) 2x +y v 3i-4j find the rate of change of fat (1,2,6) in the direction of the vector =…

A: rate of change of the function at the given point along the given direction

Q: Let F(x,y, z) = rye" – 2² Jī and P(1,0, –1).

A: Given Fx,y,z=xyey-z2x and P1,0,-1Vector u=⟨2,-3,6⟩

Q: Suppose that z is an implicit function of x and y in a neighborhood of the point P = (0, −3, 1) of…

A: Equation of a line passing through point (a, b, c) and parallel to vector <p, q, r> can be…

Q: Find an equation of the plane tangent to the Bohemian dome S described by the vector function R(u,…

A: