4.Show that the following vector fields F are conservatives and findALL f such that F = Vf.=(a)(b)(2xy+z³)i+x²j+3xz²ki+y)² XF(x, y, z) =F(x, y) ={(x, y) = R² | x > y}.(xYX: - y)2jfor all (x, y, z) € R³.for all (x, y) E U :=

As per guidelines, we can solve only first question if multiple questions are posted, please repost…

Show that the following vector fields F are conservatives and find ALL f such that F = Vf. (a) (b) F(x, y, z) = (2xy+z³)i+x²j+3xz²k F(x, y) {(x, y) = R² | x > y}. == Y (x - y)² şi + X (x − y)2j for all (x, y, z) = R³. for all (x,y) ≤ U :=

Show that the following vector fields F are conservatives and find ALL f such that F = Vf. (a) (b) F(x, y, z) = (2xy+z³)i+x²j+3xz²k F(x, y) {(x, y) = R² | x > y}. == Y (x - y)² şi + X (x − y)2j for all (x, y, z) = R³. for all (x,y) ≤ U :=

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.2: Inner Product Spaces

Problem 101E: Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that...

See similar textbooks

Related questions

Q: Evaluate the definite integral S²₁(9ti +t³j+t¾ k)dt = [[ 0 ]i] ¹₁ + [[ 0 ] i] ¹₁ + [ 0 ]i] ¹₁ = 0

Q: Find the dimensions of the box with volume 2744 cm3 that has minimal surface area. (Let x, y, and z…

Q: Find the directional derivative of the function at the point P in the direction of the point Q. f(x,…

Q: 3 2 MA 5 Based on the graph above, estimate to one decimal place the average rate of change from z=1…

A: To find average rate?

Q: 1. Find the linearization of f(x) = (x³ + 1)¹/² at x = 2 and use this to estimate f(2.05).

A: Please see the below picture for detailed solution.

Q: Which of the following conditions form the HYPOTHESIS for the basic form of L'Hopital's Rule? Let f…

A: Use the concept of L’Hopital’s rule when determining a limit.

Q: b. Use the substitution x = u² and the fact that S e-u² du VI = ¹(²-) = √². to show that I

Q: The function f has a continuous second derivative, and it satisfies f(1) = -4, f'(1) = 0 and f"(1) =…

A: The solution is shown below-

Q: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the…

A: Given: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing…

Q: A fluid moves through a tube of length 1 meter and radius r = 0.004±0.00025 meters under a pressure…

A: Given that r=0.004, ∂η∂r=0.00025, p=2×105, ∂η∂p=1000v=0.875×10-9, ∂η∂v=0And η=π8pr4v

Q: Let r(t) = (t², 1 — t, 4t). Calculate the derivative of r(t) · a(t) at t = 2, assuming that a(2) =…

Q: Consider the curves y = x^2 sinx and y = -1 - sqrt(1 + 4(x + 2)^2 ). Find the x-coordinates of…

A: To find the x-coordinates of the points of intersection of the two curves, we need to solve the…

Q: Find the interval(s) where f(x)=x²-3x³-6x² - 2x +4 is concave up.

A: Given function:- fx=x4-3x3-6x2-2x+4

Q: Construct the particular solution to the homogenoeus linear second order ODE d 2x dt2 + 10 dx dt +…

Q: Find the mass of the rectangular prism 0<x<1, 0<y<4, 0<z<2, with density function ρ(x,y,z) = x

Q: Find (without using a calculator) the absolute extreme values of the function on the given interval.…

Q: Determine whether the series is convergent or divergent by expressing the nth partial sum s as a…

A: We can prove the convergence by using nth partial sum of the given series.

Q: /transcript Perform a first derivative test on the function f(x) = x (x-3); [-3,3]. a. Locate the…

Q: Find the differences in the given base. 51 six (a) (b) (c) (d) 22 six six 501 six 222 six six 753,…

Q: Find f(x) if f"(?) = 12x^2+6x−4 and f(0) = 4 and f(2) = 10

A: f''(x)=12x2+6x-4f(0)=4f(2)=10∫xndx=xn+1n+1+c

Q: 4. How much work is required to fill a spherical tank with a radius of 1m with water (1000 kg/m³)…

Q: Evaluate the following limit. lim 1+ X→∞ lim X→∞0 1 2 3 X 2 3 X In x Inx = (Type an exact answer.)

Q: You are in charge of erecting a radio telescope on a newly discovered planet. To minimize…

A: Given: Mx,y,z=12x-y2+xz+240The radius of the spherical planet is 12 unit. Hence, x2 + y2 + z2 =…

Q: 2. Sketch the level curve z = k for the indicated values of k. 1 (1). z==(x² + y²), k = 0,2,4,6,8.

Q: For the formula at the given point, find the equation of the tangent line 5. y=x²e at the point…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: count in a bacteria culture was 900 after 15 minutes and 1800 after 30 minutes. Assuming the count…

Q: (0, 0) Corner (0, 0) (7,0) (6,2) (0, 3) (0, 3) 1 (4,4) 40 want to find the maximum and minimum…

A: To solve the following problem

Q: dy d x X Y y(0) 1 = -3

Q: І exta) (x+b) dx

A: integral

Q: As the wheel of radius r cm in the figure rotates, the rod of length L attached to point P drives a…

Q: The population of a town is growing according to the differential equation dy/dt =ky The growth…

Q: 4. Find the solution to the initial value problem y'= 5(2-y), y(0)=5. Report solutions in y equals…

Q: Consider the following graph of the second derivative, f" (x), for some function f(x): f"(x) -6 -4…

Q: (b) x2n - 2y5n 1/3 x5n + 4y² X

Q: Evaluate the integral by interpreting it in terms of areas. 6² ( 1² x - 2) αx -X dx

Q: (a) Find an equation of the tangent plane to the surface at the given point. z = x² - y², (3, 2, 5)…

Q: If f(t) = (t² + 6t+4) (2t² + 2), find f'(t). Find f'(3). Question Help: Video Message instructor…

Q: What is the vertical asymptote for the function f(x) = 1 4x Ⓒx=0 x = 1 x=4 y=1 ? 61

Q: PLS do fast within 5 minutes and i will give like for sure Solution must be in typed form The…

A: How can both x-intercept s be determined if the equation y=-(x+6)(x-3) is given?

Q: 112. Gaussians An important function in statistics is the Gaussian (or normal distribution, or…

Q: Given that the acceleration vector is a(t) = (−1 cos (−1t))î + (−1 sin (−1t))ĵ + (−5t)k, the initial…

Q: 9. At time t= 0 a particle is at the origin. It then begins moving along the positive x- axis so…

A: For part (a):

Q: Which of the following conditions form the HYPOTHESIS for the basic form of L'Hopital's Rule? Let f…

A: Use the concept of L’Hopital’s rule when determining a limit.

Q: The price, in dollars per units, that consumers are willing to pay for a popular high-end digital…

Q: 3. Write a polynomial of lowest degree with zeros of 5 (multiplicity 2) and -3 (multiplicity 2) and…

A: To write a polynomial of lowest degree with zeros of 5 (multiplicity 2) and -3 (multiplicity 2) and…

Q: A ball is thrown upward. Its height hin feet is given by h(t) = 104t - 16t², where t is the time…

A: Given height:- ht=104t-16t2

Q: Evaluate the limit for the graph: lim f(x). X+2+ O -4 +00 0-1 01 -00 4 2 -20 -2 24 4 8

Q: Find all critical points of the following functions. a. f(x) = -r² + 10x + 43 b. g(x) = ¹/3 c. h(r)…

A: To find the critical points for given function

Q: 1. Find all critical numbers of the function f(x) = 1/3 sin (6x) -x, on the interval 0<x< Show all…

Question

4.
Show that the following vector fields F are conservatives and find
ALL f such that F = Vf.
=
(a)
(b)
(2xy+z³)i+x²j+3xz²k
i+
y)² X
F(x, y, z) =
F(x, y) =
{(x, y) = R² | x > y}.
(x
Y
X
: - y)2j
for all (x, y, z) € R³.
for all (x, y) E U :=

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here