(b) Given the force field F(x, y, z) = (z³ – 2xy)i – x²j + 3xz² k (i) Show that F is a conservative vector fields (ii) Find its potential function (4)

Q: Find the gradient vector field of f(x, y, z) = 9x5 + 7y3 + 6z?

A: To find the gradient of  f(x,y,z)=9x⁵+7y³+6z²

Q: Find the work done by the force field F(x, y) =(2y'+2xy, 6xy+x +1) in moving a particle over the…

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Q: Consider the vector-field F = (2 — ysinr − 1) + (cos x − y ). – - (a) Show that this vector-field is…

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Q: 9. Compute the flux of the vector field F(x, y) = (-x sin(1+xy) – 4 cos(TY), y sin(1+ xy) + 6x)…

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Q: Consider the vector field F(x, y,z)= 2.xy i+(x² +z² ) j+2yzk. c) Is F a conservative vector field?…

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Q: 1- Prove that the force field F known as : Prove that the force field defined by F = (y*z' -6xz? )i…

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = ln(x + 5y + 6z). F(x, y, z) = =

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Q: Prove that F(x, y, z) = (y² cos x + 2*)i+ (2y sin x – 4)j+ (3xz2 + 2)k - is a conservative vector…

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Q: Find a potential function for the vector field F(x, y) = (14xy + 7y- 8, 7z + 7z). f(x, y) =

A:

Q: (a) Suppose a vector field F(x, y) construct a potential function o(x, y). i+ is conservative. Then

A: Consider the given vector field.

Q: 3 , find a potential function for the vector field F by inspection or show that one does not exist.…

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Q: Choose a correct potential function for the conservative vector fieldF = (3x-y+1, –x-4y-2).

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Q: Find the potential function p, for the conservative vector field F(x, y, z) = (2xe² – y²sin x)î +…

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Q: 4. The vector field F(x, y) = (x² – y²)i+ 10-Rj-2zrk represents the velocity of a gas flowing in…

A:

Q: Determine whether the vector field h(x,y) = y^2i + (2xy-e^2y)j is conservative or not. If it is…

A:

Q: A) Consider the vector-field F(x, y) = 2xy³i+ 3y²x²j. 1. Show that F is conservative. 2. Find a…

A: The given vector field is  F⇀(x,y)=2xy3i⇀+3y2x2j→ We have to show that F→ is conservative

Q: b) Show the force field (x, y, z) = (x²y + In(yz)) i+ + y cos(2z) ) j+ y? sin(2z) 3 F k is a…

A:

Q: Determine whether F(x, y) = xi +9yj is a conservative vector field. If so, find a potential function…

A:

Q: (a) Is the vector field | F(x,y) = (xe, ye²) conservative? Justify your answer. If it is…

A: Let the vector field F = Pi + Qj.The above vector field is conservative if and only if dPdy=dQdx

Q: Find the gradient vector field of f(x, y, z) 5x+ 2y+8z

A:

Q: Q3) Determine if the vector field F(x, y, z) = (yz,xz + 2y, xy + 1) is conservative. If it is, find…

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Q: Calculate the work done by the vector field F(x, y)= ,2xy) on a particle that moves once around the…

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Q: Find a potential function for the conservative vector field. F(x, y) = xex*4Y(2yi + xj)

A: If curl f is zero then conservative field

Q: Q1. What is vector field and potential function? Sketch the gradient field of p(x, y) = x² + y² –…

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

Q: (1) Let F(x, y) = (2y³/2, 3x√√y). (a) Show that F is a conservative vector field. (b) Find a…

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Q: Show that the vector field F(x, y, z) = (le* cos y + yz)i+(xz - e* sin y)j+(xy + 4z) k is a…

A: Given: F(x,y,z)= (excosy+yz)i+(xz-exsiny)j+(xy+4z)k To show that F is conservative and if it is,…

Q: the gradient vector field of f(z, y) = In(x + 4y) %3D Work

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Q: Find a potential function for the conservative vector field given by y3/2 2T 2 2x sin z F(r, y, 2) =…

A: We will find out the required potential function.

Q: 2. Given F(x, y) = (4x³y² - 2xy³)i + (2x¹y − 3x²y² + 4y³)j is a - conservative vector field. a. Find…

A: To find the potential function for the given conservative vector field :-

Q: b) Verify whether the vector field F is conservative, if so, then find the potential function F = (…

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = In(x + 3y + 4z) . F(2, y, 2) =

A:

Q: Determine whether F(x, y) = 3xi + 7yj is a conservative vector field. find a potential function for…

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Q: Find a potential function for the vector field F(x, y) = (6x sin y, 3 cos x ), if it exists. A. No…

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Q: What is vector field and potential function? Sketch the gradient field of p(x, y) = x² + y² – k².

A: If z=f(x,y), then the variables x, y are called the input of the function, and z is called the…

Q: determine if the given vector field f is conservative and hence find the potential function for the…

A:

Q: Q1. What is vector field and potential function? Sketch the gradient field of p(x, y) = x² + y² -k².

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

Q: 3. Find a potential for the conservative vector field: F(x, y, z) = (2xy + 2x, x² – 2yz³, -6z –…

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Q: ind the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

A: The gradient of a function is the rate of change of a function and for a function, f(x,y,z), the…

Q: Determine if the vector field F(x,y,z)= (yz,xz+2y,xy+1) is conservative. If it is, find its…

A:

Q: If F = (4xy – z³) î + 2x² ĵ – 3xz² k is a conservative force field, then scalar potential of F is…

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Q: b) Verify whether the vector field F is conservative, if so, then find the potential function F = ,…

A:

Q: Determine the total work, by Green's theorem, done by the force field F(x, y) =, on a particle…

A:

Q: Determine whether F(x, y) = e cos 9y i – e" sin 9yj is a conservative vector field. If so, find a…

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Q: Show that the vector field F(x, y, 2) = (2x cos y – 3)i – (x² sin y + 2²)j – (2yz – 2)kis a…

A:

Q: Suppose a vector field F(r, y) = construct a potential function o(r, y). i+ j is conservative. Then

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Q: Determine whether F(x, y) = e5 cos 5y i – e5" sin 5yj is a conservative vector field. If so, find a…

A: ANSWER :

Q: (b) A potential function for the vector field F (x, y) = (2x + 1)(x² + x + 1)² 7+ (2y + 1)(y² + y +…

A:

Q: 2: Compute the work done by the force field F = (y, -x) to move an object from point A = (1,0) to B…

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Q: Determine whether the vector field…

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Q: a) What is the flux of the constant vector field F = (a, b, c) through any closed surface? b) Is the…

A: Given That : A constant  vector field F=a,b,c and F=x3,y3,z3 To Find : i) The Flux through of…

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.