ri + yj F(r,y) (x2 + y2 + 1)?

Q: (x,y) = xy i + x+15 yj, on R'. Find a potential function for

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Q: Let I = f x*cos(x) dx. The approximation of I using the two-point Gaussian quadrature formula is:

A:

Q: F(x, y) = (8xy° + 3)i+ (12x²y² + 2e2")j is conservative by finding a potential function f for F, and…

A: Given that, Fx,y=8xy3+3i+12x2y2+2e2yj⋯⋯(1) C: rt=2sin5ti+2tπsin85tj 0≤t≤π2S Let, F=Mi+Nj Where,…

Q: b) Find the potential P(x,y) attached to the exact ODE 2r sin(y) + x* cos (y) y = 0

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Q: (a) Find the gradient and Laplacian of the scalar function T(r,0,¢) =r(cos0+sin0cosø)

A: As two questions are given I will solve only the first: We are given: T(r,θ,ϕ)=r(cosθ +sinθcosϕ)…

Q: 3. For all a? + y + 2? > 0, verify that the velocity potential 1 $(r, y, z) = Vr? + y² + z2 is a…

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Q: Demonstrate that the functions Y1 = a", y2 = sin(x), Y3 = xe* are linearly independent on R. 9.

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Q: Find a potential function for F or determine that F is not conservative. F = (cos(z), 16y, -x…

A: The vector field given in the question is: F = <cos(z), 16y, -xsin(z)> Hence, F1 = cos(z), F2…

Q: Let flxiy) = Rx Jy 27 %3D a) Finid the gradrent of f b) Find the directional derivative of f at the…

A: Consider the function as  fx,y=2xy

Q: Use a local linear approximation of the function f(x) = VI cos[(V2x)T] approximate v3.98…

A:

Q: (B) Find the potential function V = V(r, y) such that %3D + yi+ + r)j = V¥ 1+ x2 + y? 1+ x? + y? and…

A: We have to find the potential function ψ=ψx,y such that x1+x2+y2+yi+y1+x2+y2+xj=∇ψ and also evaluate…

Q: Show that F. dr is independent of its path, given that F(л, у, 2) — + tan 1+x² 2) i+ tanrj+ k. 1+2²…

A: We will show the required result.

Q: If F (r, s, t) = s? î + (2rs + e3t) ĵ + 3se3tk, find potential function f (r, s,t) such that F = Vf.

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Q: Using an appropriate linearization, the local linear approximation of f(x)%3D+ cos r at is 2.

A: To determine the linear approximation of the function.

Q: Find a potential function for F or determine that F is not conservative. (If F is not conservative,…

A: Given Data The function is F=<6zsec²(x), 6z, 6y+6tan(x)>.   The curl of the vector field…

Q: Let F(x, y) = (4ye*y – 3x², 4xe*y – sin y). %3D a. Find a potential function of F. b. Find S„F· dR…

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Q: Show that the function f(x, y, z) = x² + y² – 222 sat isfies the Laplace equation. - Good Luck.

A: Given function f(x,y,z)=x2+y2-2z2. We have to show function satisfies the Laplace equation. A…

Q: F(x, y) = (4ry³ + 3)i+ (6x²y² + 2e²w)j is conservative by finding a potential function f for F, and…

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Q: Let f(x, y) = 8x + 2y2, r(t) = (cos(t), sin(t)). Use the Chain Rule to calculate f(r(t)). !! dt…

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Q: Let F = (e" sin y) i+ (e cos y + y)j. Answer the following questions. (a) show that is F…

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Q: Find the potential function of F(x,y)=(5+8xy²,8x*y), i.e. a function @, so F =V@ Use the potential…

A: Given F(x,y)=(F1(x,y),F2(x,y))=(5+8xy2,8x2y) So  F1(x,y)=5+8xy2 F2(x,y)=8x2y ∂F2(x,y)∂x=16xy…

Q: Show that the function f(x, y) = e-2y cos 2.r satisfies the Laplace equation.

A: use partial derivative to check whether it  satisfy the equation or not

Q: Given that F = (4y² +e") ï+ (xe" +8xy) j, calculate the line integral So F • dr exactly, where C is…

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Q: F(x, y) = (8xy + 9)i + (12x²y +22)j is conservative by finding a potential function f for F, and use…

A: Given : F(x, y) = (8xy³ + 9)i + (12x²y² + 2e2y)j

Q: Use a local linear approximation of the function f(z) = VI cos[(V2r)] at some approximate v3.98…

A: To use local linear approximation of the below function to approximate 3.98cos7.963π. fx=xcos2x3π

Q: Find the potential function for F(x,y,z) = (x^-1z)i + (y^-1z)j + ln(xy)k. Show all steps and explain

A: Potential function of  F, is f such that ∇f=F.

Q: Let f(x, y, z) = x² + 2y+ e³=2« + 2°. Find the rate at which f is changing at (1,2, –1) in the…

A: Use the formula of the directional derivative and simplify.

Q: Find the potential P(x,y) attached to the exact ODE 2x sin(y) +x² cos(y) y' = 0

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Q: Let F(t) = %3D F(t)dt (don't include the +C) Find

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Q: find the potential function for F=(6x+5y)i+(5x+4y)j Select one: a. Non of them b. f(x,v) = 3x²…

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Q: Let F = (e" sin y) i+ (e cos y + y)j. Answer the following questions. (a) show that is F…

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Q: Let u(t) = 2t°i+ (t - 1)j- 8k. Compute the derivative of the following function. %3D (118 + 7t) u(t)

A: First we have to multiply the given function and then calculate it's derivative

Q: 5. Let f(1, y) = re" + cos(ry) and P: (2,0). A. Find the directional derivative of f at P in the…

A: Given information: The function is f(x,y)=xexy+cosxy and P:(2,0) and the vector is v=3i-4j. (a) To…

Q: In Exercises 27 and 28, find a potential function for F. {(x, y): y > 0} 27. F = i+ y2 (5 + 28. F =…

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Q: 1. (a) Let /(r,y)- cos(z + 2y). Compte the directional derivative Da/(r.y), where u- (b) Compute ff,…

A: Given that, In part (a), f(x, y) = cos(x+2y) u=(x,y)=-12,12 We have to find the directional…

Q: EX 3! Show that F (x₁y) = (2xy - 3) + " + (2y + x² ) 5* is conservative and find a potential of it..

A: Use the partial derivative for finding the potential function

Q: Find the linearization L(x,y) of the function f(x,y) = e* cos (9y) at the points (0,0) and ...

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Q: Use a local linear approximation of the function f(x) = Vr cos[(V2x)] approximate v3.98…

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Q: F(x, y) = (8xy' + 8)i + (12x²y² + 2e²)j is conservative by finding a potential function f for F, and…

A: We have used the conservative vector field formula since F is conservative vector field then we…

Q: b/ Show that the function satisfy Laplace equation f(x, y) In /9xy+3y2

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the potential function for F(r, y) =. Select one: O A. f(r,y) = ev + sin y- c O B. f(r,y) = e²y…

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Q: Using an appropriate linearization, the local linear approximation of is f(x) = T+ cos r at 2.

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Q: [4xy + 2x] 5) Let F(x, y) =[ 2x² + 1 Is F conservative? If so, give a potential function for F. %3D

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Consider the function g(x) = 5 S cos t dt – x?. Then g' (x) is

A: Given gx=12∫x4x2costdt  -x2

Q: Consider r (t) = ( – 4t² + 3, 2e“, 4 sin(5t)). Find F(t)dt. Don't include the +C. frwa = %3D

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Q: Given that F(x, y, z)=sin x i+cos yj+ xzk. Evaluate , F.dr where C is given by r(t)={r',-f,t) :…

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Q: Give a physical interpretation of JT. F.ndS.

A: This expression is of surface integral for calculating the area of the field bounded in the…

Q: Determine if F is conservative, if it is then find a potential function. (a) F = (b) F = (c) F =

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Q: Let g(u, v) = u² + v³, 2(t) = cos(1), v(t) = In(t). Compute dg (please use only the dt your…

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.