The vector field F(r, y) = (2xy +y) dx + (æ + 2xy) dy is conservative. %3D The function f(x, y) = x² + 2xy+K is a functionf such that F =Vf. %3D Evaluate F dr, where C is the line segment from (-1, 1) to (2, 2).

Q: Vz(x, y) V + y have the Show that all the vectors in vector field F same length, and state the…

A: The length or magnitude of a vector a, b is defined as follows: a, b=a2+b2 Note ca, b=ca, b, where c…

Q: The smooth vector-valued function P(t) satisfies P(2)= (-4, 8,-7), P′(2)= (0,-5,2), and P'(2)= (3,…

A:

Q: Sketch the vector field F. F(x, y) = yi + xj √x² + y² 2

A: Given:The vector field  is given by .To Find:We have to sketch the given vector field.

Q: Find the gradient vector field of f(x, y) = ln(5x + y)

A:

Q: Represent the following equations in R? by a vector-valued functions. Imet gaoglecomis shwing your n…

A: Given

Q: Let f(x,y) = sin x+sin y. (NOTE: You may use software for any part of this problem.) %3D (a) Plot a…

A: (A) plot the contour of f.

Q: Find r(t) ∙ u(t). Is the result a vector-valued function? Explain.…

A: Given:r(t)→=(3t-1)i^+t34j^+4k^u(t)→=t2i^-8j^+t3k^To determine:r(t) →. u(t)→

Q: Compute ∇ƒ(-1, 2, 1), where ƒ(x, y, z) = xy/z.

A: Given,f(x,y,z)=xyz     As we know ∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z

Q: Sketch the vector field. 8 2 0 -2 0 y 0 2 0 -2 F(x, y) = (2, 2) = 2'

A:

Q: Find T(t) ,N(t),B(t), and K(t) for the vector position r(t) = (e2t cos t) i + (e2t sin t)j + 2k when…

A: Given rt=e2tcosti+e2tsintj+2k

Q: calculate div(F) and curl(F). F = (xy, yz, y² – x³)

A:

Q: Consider the following function. T: R? - R, T(x, y) = (2x?, 3xy, y²) Find the following images for…

A:

Q: Sketch the vector field. F(z, y) = (- 2 2 2 0 2 -2 0 -2 2 -2 2 -2 -2 2 -2 4- -4 -3 -2 -1 2 3 -2 -3-…

A:

Q: The graph of the vector function r(t) = ti +t²j+2k is

A: Graph of vector function  r(t) is :  r(t)= t i + t2 j + 2k

Q: Find the domain of the vector function. lim t->infinity

A: Answer

Q: Consider the vector-valued function r(t) = 4t²i + (t5)j + tk. Write a vector-valued function u(t)…

A: Topic: vector valued function

Q: iven belo

A: The value of derivative of vector R→t, R'→t=2e2t-4,6t2,1t-1  Integrating the derivative vector with…

Q: Find the domain of the vector valued function. r(t) = 3/(t-4) i + sqrt(3-t) j + ln|4-t| k.

A: Given vector valued function r(t) = 3(t-4) i + (3-t) j + ln|4-t| k We know domain of a vector valued…

Q: Why is r(t) = ⟨ƒ(t), g(t), h(t)⟩ called a vector-valued function?

A: Given r(t) = ⟨ƒ(t), g(t), h(t)⟩. We need to give reason why r(t) is called vector-valued function.