2.31 Let A and B be vector functions of position vector x with continuous first and second derivatives, and let F and G be scalar functions of position x with continuous first and second derivatives. Show that: (a) V. (V x A) = 0. (b) ▼x (VF) = 0. (c) V (VF x VG) = 0. (d) V. (FA) = A·VF+ FV.A.

Q: Determine the domain of the vector function r() = cos(4t) i + 7in(t - 5) J - 10 Evaluate if the…

A:

Q: Compute the derivative of the vector-valued function r(t)=⟨sin2t,et2⟩.

A: In order to compute the derivative of the vector-valued function: Differentiate the vector function…

Q: (플몰) V2 v2 2' 2 f(x, y) = x² – 3y², u и —

A:

Q: Find the velocity and acceleration vectors and the equation of the tangent line for the curve r(t) =…

A:

Q: Derivatives of vector-valued functions Differentiate the following function.

A: We have given the function;

Q: Let h(x, y) be a differentiable function and let (xo, yo) be a point in the domain of h. Also, let u…

A:

Q: If the gradient of f is Vƒ = z j - yi – 2xzk and the poi f(x, y, z) = 0, find an equation for the…

A:

Q: Find the approximation for the Green's function of the one-dimensional acoustic wave equation in the…

A: Given function is, cx=aebx Here, a>0 and it's constant here we have to see the effect of b so,…

Q: Let r(t) be a vector-valued function such that the magnitude of r(t) does not change over time. Use…

A: if r'(t) = 0 then we can say that r'(t) is perpendicular to the function r(t) for all times t.

Q: (b) Find the directional derivative, Daf(2, 9) where u is a unit vector in the direction of i = 31-…

A: (a) Consider the function fx, y=xy. This gives ∇fx,y=i∂∂x+j∂∂y fx,y=i∂f∂x+j∂f∂y=yi+x2yj   At 2, 9,…

Q: 1. Let ř(t) = (In |t – 1|, e', vi ) (a) Express the vector valued function in parametric form. (b)…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Directional derivative of f(x,y) at any point P in the direction of vector v is, =(∇f)P.(unit vector…

Q: ) Find the directional derivative of the function f(x, y) = sin²(xy) at the point P (2,7) -2i+j √5…

A:

Q: . Use the gradient vector to find the directional derivative of f (x, y) = at x2-y the point (1, 2)…

A: