Question 25 Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. (3.0).(-7), and (0.7) 0, F = sin 5yi + cos 9xj; C is the rectangle with vertices at (0, 0), O O 25 O TT 4|5

Q: Construct the inverse matrix (if it exists) for the following matrices: [12 61 (а) А %— 4 2. 1 -2]…

A: We will find out the required solution.

Q: b) Show that F - dr is independent of its path, given that y F(r, y, 2) = 1+. + tan-2) i+ tanrj+ k.…

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Q: Show that the work of F = (2³-y³)i + (2³-y³)j on c, the unit circle centered at the origin with…

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Q: 5. Let f(2)=. Use the polar form of the Cauchy-Riemann equations to determine where f is…

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Q: Find the Laplace transformation of the unit impulse function 8(t-22017) and The unit step function…

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Q: Consider the shaded square region on the s-plane, as shown in Fig. Q1. Let p =-Co, + j@, 1-5?, S'-…

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Q: h) Find a parametric representation of the Parabolic equation z = 9(x² + y²)

A: Parametric representation of the Parabolic equation z = 9(x² + y²) will be cartesian coordinates as…

Q: Use Green's Theorem to evaluate F. dr. (Check the orientation of the curve before applying the…

A: We have to evaluate the integral using Green's Theorem.

Q: F. dr. (Check the orientation of the curve before applying the theorem.)

A: Given,          F(x, y)=e-x+y2, e-y+x2 and C consists of the arc of the curve y = cos(x) from -π2, 0…

Q: is the following function analytic (Express your answer in polar form) f(z): = y - ix x² + y²

A: We can solve this using polar form of analytic function

Q: Show that F dr is independent of its path, given that F(r. y. :) = ( i+ tanrj+, + tan k. 1+:2 %3D…

A: Here we will find out the required value and prove the result.

Q: Let f(z, v, z) - Y+2'and z- st", y= st, and z – 8, () Calculate the primary derivatives 372 (b)…

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Q: Demonstrate that the Simple Rotation Theorem holds true: Tf = ŕ cos 0 - ¯ × û sin 0 +ř · ūū(1 − cos)

A: Given: rf¯=rcosθ-r×u⏜ sinθ+r·u u(1-cosθ)We need to demonstrate that the simple rotation theorem…

Q: 7. If f is a scalar field and v = [v1, v2, v3] is a vector field, show that div(fv) = fdiv(v) +v •…

A: We will use simple definition of divergent of vector quantity and gradient of scalar quantity.

Q: Determine the image of the set of points |z| =3, -\pi/4 <=θ <= 3pi/4 under the reciprocal…

A: Step 1:Given that ∣z∣=3⟹z=3eiθ,−4π​≤θ≤43π​ Step 2:Now the reciprocal mapping is…

Q: b) Find v²f where f = e²x sin2y. cl Write the sufficient condition for ovistence of Lapla

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Q: Find the ccw circulation of F = around the curve C: from (0, Guam ( %3D

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Q: (a) Show that v.ve =p²o, where v- S+ denote the Laplacian operator

A: We will prove the following result.

Q: Consider the function f(x,y) over the domain D enclosed by the 1+ x2 + y² polar curve r =2+…

A: (a) Look at the level curves of the function within the domain D.    The boundary of the domain D…

Q: a) Find the Laplace transformation of the function f(t) = cosh at sinh bt

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (c) Determine the…

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Q: Find pairs of solutions of Laplace's equation, =0, based on these complex functions (a) ze2, (b) z*:…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3 Substitute Z=x+iy in Ze2z…

Q: a. State the amplitude and period of the function f: R R, ƒ (x) = 3 – 6cos TEX Find the general…

A: Given function f(x) = 3 - 6cos(πx/4)

Q: If the given three vectors are coplanar, then find the value of x. A = i-2j + 3k, B = xj + 3k, C =…

A: A, B, C are coplanar.So

Q: Let w where z = rei0. 1) Show that by using Cauchy Riemann Equation (C.R. Eq.) in polar form that w…

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Q: g) Find the Fourier sine series of the function f(x)=-100¹0(-<x<n); f(x)= 100¹0 (0<x<n)

A: We have to find the Fourier sine series of the function  f(x)=-10010if -π&lt;x&lt;010010if…

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: Use Green's Theorem to evaluate ſ F•dr. (Check the orientation of the curve before applying the…

A: To find- Use Green's Theorem to evaluate ∫CF·dr. (Check the orientation of the curve before applying…

Q: Write the sufficient condition for existence of Laplace transformation of a function.

A: We know the definition of Laplace Transform ,  The Laplace Transform is a linear operator that…

Q: 1. Find the tangent vector to the curve 6t r(t) = [t³ – t, t+1 , (2t + 1)*] at t = 1.

A: As per our guidelines we are supposed to answer only one question. If you want solution of any…

Q: 2. Let F(t) = (et cos t) î+ (e¹ sin t) ĵ + et k. a. Find symmetric equations of the line tangent to…

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Q: (1; 0 4

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