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Q: Prove the absorption law of x + xy = x using other laws of identi

A: to prove x+xy=x x+xy=x1+y use the identity law x+0=xx·1=x hence,  x+xy=x·1+x·y

Q: Laplace equation on a rectangle Aµ = 0 Δμ Solve: {u(x,0) = µ(x, 1) = 0 on [0,1]? ιμ(0, y) - sin…

A: Taking b as constant. So, we need to solve,            .

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Q: Derive the De Moivre's Theorem with detail Explanation?

A: Statement: For any real number x, we have (cos x + i sin x)n= cos(nx)  i sin(nx) Or, (eiθ)n=eiθn…

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A: here we have to find the unit tangent vector , also find the length of indicated portion of the…

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Q: of Jelution Discuss passibility of existence ux)= Sinfox +257 K(1,)u() dt %3D Sn(t+ /4) Sin (x-E);…

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Q: Accelerati on of gravity g(x)= GM.X if oŹx< R GM x2 if xZ R R= radius of Earth, M = mass of Earth G…

A: Consider the given function and determine the values of the function for x &lt; R and x &gt; R.…

Q: a2u, a2u = -2; 0<x< 1, 0 < y<1 condition u(x,0)= u(x, 1)= u(1,-x) u(0,y)= 0, u(1,y)= sinh(IT) sin…

A: Given: ∂2u∂x2 + ∂2u∂y2 = -2   0&lt;x&lt;1, 0&lt;y&lt;1 ---------(1) with boundary condition…

Q: 4. Find the tangent plane to the function f(x, y) = xy+x at the point M = (-1,1) in the form Ar + By…

A: Explanation of the answer is as follows

Q: Topic: Incentives ( Proof of integration formula for hyperbolic secant and hyperbolic cosecant)…

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Q: Laplace's equation Verify that the following functions satisfy au, u 0. ax²' ay? Laplace's equation,…

A: Given Equation: ux,y=lnx2+y2 Laplace equation ∂2u∂x2+∂2u∂y2=0 Partially differentiate ux,y to second…

Q: Qi find Laplace Tranform for the fllowing functivas e f 4)= t ést sinzt - 34 -t ® PCt) = t e %3D

A: Note- As per our company guidelines, we are supposed to answer only first 3 sub-parts. Kindly repost…

Q: Length of curves Use a scalar line integral to find the length ofthe following curve.

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Q: Discuss passibility of existence f Selution u(x)-Sin10x t257 %3D K(z,t) = Sin(x+7) Sin[t-)3; 0xct…

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Q: sin? Of + cos? 0i F = A pn where A is a real constant. Compute the flux of F through a spherical…

A: The general form of a three dimensional vector-valued function in spherical polar coordinates is…

Q: Bessel's Function Tutorial sheet J, (x) Find ý and ý 2. y =

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Q: solute value of the Jacobian ) for the chang Ə(s,t) I = s -ť, y =t sin(s).

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Q: Using Cauchy's integral formula (chapter 14.3), integrate counterclockwise -dz z2 + 4z + 3 where C…

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Q: 5. f (t) sinh 3t + cosh 3t – 2t3

A: This is a problem Laplace Transform.

Q: cot z• 2z dz In sen z' + c 33. cot x' dz %3D 1/2

A: see below the answer

Q: = ² - 3 and ro = 3. Use Newton's method to approximate v3 by letting f(x) Find z and r2.

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Q: Topic: Incentives ( Proof of integration formula for hyperbolic secant and hyperbolic cosecant)…

A: To prove:-

Q: 10. Show that the function f(x,y, z) = z arctan satisfies the Laplace equation.

A: We have to cheek

Q: Using the Cauchy-Riemann Equation. u=x^2-y^2-2y show that is harmonic. Find the function v whose…

A: We have ,  u = x2 - y2 - 2y We need to show that , u is harmonic. We know that , A function  u(x ,…

Q: 1. Find the exact maximum value and exact minimum value of the function on the given interval.…

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Q: Determine of the equation below satisfies Cauchy-Riemann's Equation. f(z) = cos?(z),where z = x + yi

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Q: 9.) A particle moves in a straight line according to the law of motion: s=cos(x). a. Find the…

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Q: Theorem-e Caley-Hemiltion)let Arxz motrix OAntra +detA=0 tet Azximufrix

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Q: Torsion of a helix Compute the torsion of the helixr(t) = ⟨a cos t, a sin t, bt⟩, for t ≥ 0, a &gt;…

A: Position vector - r(t) = acost, asint, bt Formula for finding the torsion is given by - ζ =…

Q: Theorom:- Let f-3GDCI); XoEIthen O TfaeR then a fisdefferantible at (a P) (xo)= QP(xo) D ft…

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Q: theorom J f E Riemann La,b] and feas>o for xE Ľ q,bJ then a

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Q: ez - w = tanh z = ez + e 1 w = coth z: tanh z 1 w = sech z cosh z 1 w = csch z sinh z Example: prove…

A: Since you have asked the multiple question as per our policy we will solve first one for you if you…

Q: Can i get help step by step

A: The linearization of the function f(x) at x=a is determined by, L(x)=f(a)+f’(a) (x-a).

Q: Bessel's Function Tutorial sheet 2. If x Jg, (x) Find ý and ý %3D

A: Solution:-

Q: Q: Using lagrange's theorem prove that 0. 1+ r

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Q: y' + 2xy = 2x³, y(0) = 1, y(2) using h = 0.2 %3D %3D

A: We have to use the Euler's method to find the value of y at x=2 for the differential equation…

Q: In calculus the curvature of a curve whose equation is by y = f(r) is defined to be the number…

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Q: Solue using laplace fransforms +y = 1 co) =j co) = co

A: Concept:

Q: interal [ozd Upper Rucimann Suns f(akx²tx »- Caletete the Lowe intertal [0,2] Upper Riemann Snas…

A: Solution is written in below steps.

Q: Find (do not do the Newton's iteration) the con- vergence order and the rate of the Newton's method…

A: See answer below.

Q: At time to, a moving particle has the velocity vector v = 5i and the acceleration vector a = 3i +…

A: Given, At time t0, The velocity vector, v = 5i The acceleration vector, a = 3i+4k Formula for the…

Q: 0 1+x

A: For the above-given question, the answer is as shown below.

Q: Find all the singularities of the f(z). Are they isolated? sin z z3(z – 3i)² sin f(z) = Classify all…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 7. An object is propelled upward at an angle 45° s x< 90°, to the horizontal with an tnitial…

A: Given that Rθ=v02216cosθsinθ-cosθ

Q: Using the metric - [12 4 G =| 4 1 1 (x')²] Calculate the length of the curve given by x' = 3 - t x2…

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