Find the directional derivative of the field f(x, y, z) = In(4 x) at P = (1, –2, –5) in the direction a = (4,–3, –3). Give an exact answer. D(1,-3,–3)/|(1,-2,-

Q: Make a sketch of the following vector field. F= (2y.x)

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Q: Q1(a) For which value of a the field v = (y-x)i +(2x- y)j+azk is solenoidal. (b) Find the gradient…

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Q: Find the Laplace transform of 1._ f(t) = [1 − U₂π(t)](2 sin t — sin 2t)

A: According to Bartleby policy, " if there are more than 1 question, then we are advised to solve only…

Q: Q4: Find the curl of the vector field F(x, y.2) = x*/yi +j+ zk at the point(2,4).

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Q: Find an expression for the vector field F = ⟨x - y, y - x⟩ (in terms of t) along the unit circle…

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Q: Find the gradient field that corresponds to function #(x,y,z) = y² – x² + x e=² – y³ z

A: The gradient of a scalar point function f(x,y,z) is given by; Grad (f)=∇f=∂f∂xi+∂f∂yj+∂f∂zk

Q: Evaluate F. dr for the vector field F(x,y) = xy²i+ x²yj where C is given by r(t) = cos (t)i + 2 sin…

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Q: Find the gradient field of the function, g(x.y,z) = e 22 - In (3x² + 4y²). The gradient field is Vg=…

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Q: For the following practice question, please determine whether the vector field is conservative. If…

A: We have to find potential function

Q: Find the Laplace Transform of f(t) = cos t u(t-1)

A: The given function is f (t) = cos (t) u (t – 1):   Find the Laplace transform of the given function.…

Q: A vector field F = x(x² – y²) + ŷ(2xy + y?) a) f d.č =? c on the closed curve in the figure b)…

A: a) Consider the figure:

Q: 8. The component of the field F= (1,2,3) normal to the plane z = -3x + 3y -1 is (a) 0. (b) –2//19.…

A: If we are given a plane equation in the form Ax+By+Cz=D, then the normal vector to the plane will…

Q: Find the Laplace transform of f(t) = cos(2t) * u

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Q: Given a scalar field f(x, y)= xy + x² and C is the curve defined by the equation y =-x². Calculate F…

A: Given scalar field  fx,y=xy+x2 and C is the curve defined by the equation y=-x2.

Q: Q2: Find the work done S. F.dr in the force field F = yzî + xzĵ + xyk in moving from (1,1,1) to…

A: The equation of a line joining by the points and is given as the following.

Q: f(t) = t2 cos 2t.

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Q: Find the Laplace transform of f(t) = et + 7sin(2t). %3D ANS: F(s) 1 14 + s-4 s2 +4

A: Some formulae's based on Laplace transform are given below:…

Q: Given: r = F| i = (x, y, 2) And letting F be the vector field F = f'/rP. Please solve in general the…

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Q: (b) For the case a = 3, b = 4, and for the constant vector field F(x,y,z) = 4 1 + k , find the flux…

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Q: Q2. (a) Given a vector field, F = 2xyi + (x² + 3y²z)j+ (y³ + 2z)k. (i) Determine whether if F is…

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Q: a. f(t) = 2 cos( 120t + 45)

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Q: Obtain the Laplace transform of Ost 0.

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Q: Find the work done by the field F(x,y, z) = (6z, 12x, y?) along the curve r(t) (cos(t), sin(t),…

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Q: EX2 : Find Divergence and Curl of the field function f j = In (x? + y?)i – 2z -tan + (5z + e' cos…

A: givenf→=ln(x2+y2)i-(2zxtan-1yx)j+(5z3+eycosz)kdefinition of Divergence…

Q: 2. x(t) = e5t + cos 3t %3D

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Q: Q1(a) For which value of a the field v=(y-x)i +(2x- y)j + azk is solenoidal. (b) Find the gradient…

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Q: Find the gradient fields of the functions ƒ(x, y, z) = ln√(x2 + y2 + z2)

A: The given function is fx,y,z=lnx2+y2+z2   The gradient field of a function is represented by,…

Q: The slope field oY = f(t,y), with initial condition f(0) = 1, is shown. Find limf(t.y). dt - 10 「 ンン…

A: On the slope field draw the graphical solution with initial condition f(0)=1:

Q: Find the gradient field of the function g(x,y,z) = 8xy + 6yz + 8xz. Vg = (Type your answer in terms…

A: This question is based on gradient of function.

Q: Find the Laplace Transform of f(t) = e°(3cos t + 1)

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Q: 2z Find the gradient field of the function, g(x,y,z) = In (4x? + y?). The gradient field is Vg = (…

A: Solved below

Q: Use the method of isoclines to sketch the slope field for y =x +y-1, then draw the solutions…

A: In this question, we sketch the direction field for the differential equation y'=y+x2-1 To draw the…

Q: Q2: Find the work done S. F.dr in the force field F = yzî + xzj + xyk in moving from || (1,1,1) to…

A: The given question is related with work done. We have to find the work done ∫CF→ . dr  in the force…

Q: Calculate the work done by the field F when the object moves along the given path from the initial…

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Q: What does the slope field for dy eay look like? dr where a < 0 (that is: it's negative).

A: Given that:dydx=eay

Q: Find the Laplace transform of f(t)=u(t− 3)(2t² +1)+2e³ cos²t

A: The objective is to find the laplace transform of f(t).

Q: Find the directional derivative of the field f(x, y, z) = -4x³ + 3 xy² + 5 y³ at P = (-1,–3,5) in…

A: Given f(x,y,z)=-4x3+3xy2+5y3  we have to find directional derivative of f at P=-1,-3,5 in the…

Q: Find the divergence of the field F. yj - xk F= 1/2 +: 2 OA. 3/2 2 -X O B. 3/2 2 X -y OC. 3/2 O D. 0

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Q: 2. Find the laplace of the f(t) = t2 by using the laplace transform equation

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Q: Find the potential function f for the field F = 6xi + 6yj + 4zk. %3D

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Q: Find the Fourier transform F(@) = | f(t)exp(iwt)dt of the function 0, t 0. You might want to use…

A: The given function is ft=0t&lt;01βtt≥0, where β&gt;0. We know that the Fourier transform of a…

Q: f (t) = e2t V1 + cos 4x %3D

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Q: Find a potential function f for the field F. 7y j+ y² +z? 7z 21 F = (In x+ sec(10x + 10y)) i+ sec…

A: Given that F = (ln(x) + sec^2 (10x + 10y)) * i + (sec^2 (10x + 10y) + (7y)/(y ^ 2 + z ^ 2)) * j +…

Q: Q5: a) Show that the vector field F = (x² - y² + x)i - (2xy + y)j, is irrational.

A: Given vector field is F→=x2-y2+xi^-2xy+yj^. To show: Vector field F→=x2-y2+xi^-2xy+yj^ is…

Q: 4x Find the gradient field F = Vo for the potential function p == y F =

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Q: Find a potential function f for the field F = ey*2 (2 i + 6x j+ 10x k). +

A: First we will show that F is conservative Then finding the potential function by considering it as…

Q: Evaluate ∫C F . T ds for the vector field F = x2 i - y j along the curve x = y2 from (4, 2) to (1,…

A: Given information: The value of F=x2i+yj, x=y2 and from (4, 2) to (1, -1). Calculation: Consider…

Q: 25. Evaluate |F•T ds for the vector field F = x²i – yj along the curve x = y? from (4, 2) to (1,–1).

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