Answered: Solve the conservative vector field by…

Math

Advanced Math

Solve the conservative vector field by finding the gradient of f(x,y)=(5x^2)+3xy+(y^2)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: F(x,y) = x²yi + 3y³x²j Find the integral curves for the vector field Оа. -бу + 1 = C 6ху? b. -6ху —…

A: given vector field Fx,y=x2y i^+3y3x2 j^ claim- find the integral curves for the vector field

Q: (1) Is the vector field F(x, y) = (2æ*y^ + æ) î + (2a*y³ + y) Î conservative? Support your answer…

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Let 3 = (X'X)-¹X'Y as shown in class. Let y = w'ß, where w is a column vector. Show that Var(y) =…

Q: Let r(t) = 5e7t + e2t and y(t) = 3e2t + 1le (i) Rewrite the given functions in the vector form Y(t)…

Q: Find the equation of the gradient vector field for the function f(x, y) = – læ² + 1y and then sketch…

A: The gradient vector field of given function is -2x i + 2y j

Q: For each of the following, compute the line integral S. F dr Where Cis a curve with…

Q: 4 2 IF Ø = 2x2² - xy₁ FIND 01111 AT THE POINT (2-2,1)

Q: Show that the vector field F = (x² cos y, e+y) is not a gradient vector field. %3D

Q: 2) A particle is moving along the path given by ~c(t) = (t^4 − 4t, t^3 + t). (a) Compute the…

Q: Match each of the functions (a)-(c) with the corresponding gradient vector field from those in…

A: We have to match the gradient vector field

Q: Q and Z are vector valued functions Q(-1) = , Q'(-1) = , Q''(-1) = Z(-1) = , Z'(-1) = , Z''(-1) =…

A: Given Q and Z are vector valued functions such that:Q-1=0,0,-2Q'-1=1,-1,-1Q''-1=3,2,-2 and…

Q: 8) Find a unit vector in the direction that f(x, y, z)=2x² +6xz²-yz³ increases most rapidly at the…

A: Given: A function fx , y , z=2x2+6xz2-yz3. To Find: Unit vector in the direction of the given…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs for…

Q: Given the vector field v=⟨0,2xz+3y^2,4yz^2 ⟩. Find the line integral of the path from (0,0) to…

Q: Consider the vector field v(x)=(y/(x^2+y^2))i − (x/(x^2+y^2)) j + 4k. Calculate ∫Cv dr, where C is…

Q: This question is about gradients and directional derivatives. How can you tell the differences…

A: Gradient: Points in the direction of steepest ascent of a scalar field.Directional Derivative:…

Q: he position of a particle is determined by the vector-valued function r(t)=. Find the decomposition…

A: Given position of the particle We have to find the decomposition of the acceleration vector in terms…

Q: gravity and wind.

Q: Find the values of a, b and c that make F=-5y°z7 (ax + bx6ji - 45,8,7(4x10, 107j+ cy°z64x10, 10x7jk…

A: Given that F=-5y9z7ax9+bx6i-45y8z74x10+10x7j+cy9z64x10+10x7k we know that…

Q: Line segment D runs from (1, -4, 3) to (2, 0, -1). Determine how much work is done by the force…

Q: The gradient vector field of f(x,y)=y(2x2 -y3 ) is given by: O1. (2xy)i +(x2 -3y² »i O II. (4xy)i…

Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

Q: Find a vector that gives the direction of maximum rate of increase for the 6xyz at (-1,2,1) (a)6(2i…

A: To find A vector that gives the direction of maximum rate of increase.

Q: Let F(x, y) = ⟨xy^2+2x+1, x^2y − 3y⟩ be a vector field. Let C be the curve that consists of two line…

A: Given that Fx,y = xy2+2x+1 , x2y - 3y is a vector field. Let C be the curve that consists of two…

Q: f(x,y) = 2x3+4y3-3x2-120x-192y+5 Is f(x,y) a curve, vector field, or surface?

A: To check whether it is a curve, vector or surface. f(x,y) = 2x3+4y3-3x2-120x-192y+5

Q: Let F = (t + 4) i +² sin(41) j+ t^k, G = e' i+ 4f* cos(t) j+ e$t* k and 512 -i+ 4² j+te²ª k 1 +t H =…

A: Given : F=(t+4)i+t^ 2 sin(4t)j+t^ 4 k G=e^ t i+4t^ 4 cos(t)j+e^ 5t^ 2 H = (t ^ 5)/(1 + t) * i + 4t…

Q: Describe a non-zero vector function r(t) in R^3 whose acceleration vector a(t) satisfies a(t) =…

A: Solution is given below:

Q: consider the vector-valued function r(t) = a) State the domain of r(t) b) Identify where r(t) is…

Q: Find a potential function for the vector field .F(x,y)=

A: The vector field is

Q: Find a vector that gives the direction of maximum rate of increase for the e2y cosx at (n/4,0).…

A: Consider a function . Then the maximum rate of change of this function occurs at the direction of…

Q: Use the substitution u=-3x+2y to solvethe differential equation (-3x+2y) y'= - 1. a) Clearly…

A: Given differential equation is: -3x+2yy'=-1. Let, -3x+2y=u. Differentiate both sides w.r.t. x.…

Q: Find all points on the curve r(t) = ti + t^2 j + t^3k where its tangent line is parallel to the…

A: The curve is represented by the vector function r(t)=ti+t2j+t3k .To find the points on the curve…

Question

Solve the conservative vector field by finding the gradient of f(x,y)=(5x^2)+3xy+(y^2)

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

Expert Solution

Step 1: Given.

Given: $f (x, y) = 5 x^{2} + 3 x y + y^{2}$

To find: Gradient(or conservative) vector field of given scalar valued function.

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Please help. I'm not sure how to do a partial derivative of e^-x-y. Thank you.
Find T(t),N(t), B(t),and «(t) for the vector position r(t) = (e2t cos t) i + (e2t sin t)j +2k when ( t = 0 )
Find the derivative of the vector function
Needed to be solved correclty in 60 minutes and get the thumbs up please show neat and clean work and provide correct answer please
What is the gradient of g(x,y) = ye* and its maximum value of its directional derivative at P(0, 5)? О e"(-yi + j) and /24 О e(-yi + ) and /26 e-X(-yi+j) and /26 Ое "уi-) and /24 Moving to the next question prevents changes to this answer.
Let the position vector (with its tail at the origin) of a moving particle be~r(t) = t^(2)ˆi − 2tˆj + (t^(2) + 2t)ˆk, where ~r(t) is measured in meters and t is measured in seconds.(a) Show that this particle passes through the point (4, -4, 8). At what time does it passthrough the point?(b) Find the velocity vector and the speed of the particle at time t.(c) Find the velocity vector and the speed when it passes through the point (4, -4, 8).