Let (Wt, t≥0) be standard Brownian Mot

Q: Use Stoke's Theorem to evaluate Į F· dr where F (x, y, =) = , and C is the triangle with C vertices…

A: given Fx,y,z=z2,y2,xy ⇒Fx,y,z=z2i^+y2j^+xyk^ and a traingle C with vertices 1,0,0 ,0,1,0 ,0,0,2 to…

Q: ield F = (A, B, C) such that A = 2zx, B = 3z + 2y, 0,0,0) = 1 and C is independent of

A: We have to find the following conditions according to the given information

Q: prs is Linearly independent. please prove it. z set A is orthogonal if Por every Xy>X_eA, we have 2.

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Q: Example 28: If u is moment about origin, prove the rth that r-1 Σ H-j Kj; where Kj is the jth…

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Q: #33

A: Consider the given figure.

Q: Q2. (e) Verify that the Cauchy-Schwarz inequality holds. įu=(-3,1,0), v=(2,-1,3) u u=(0,2,2,1),…

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Q: non -CentYal moment for An B (u,p) ECx³)?

A: Given; X~Binomial(n,p)The probability mass function of X is given by;P(X=x)=nxpx(1-p)n-x,…

Q: BCs: u(0, t) =u (I, t) = 0, t>0 ICs: u (x, 0) = ƒ(x), u,(x, 0) = 0,

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Q: [cos w ((t1 -t2 Prove that Covariance (t, , t) = Auto correlation (t, , t2) = %3D %3D

A: Answer: For the given data

Q: O Grven rref(A)=.] and A represents for mation T: R→R, Tlu)=Au. State all rectors in Show work and…

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Q: a) Rewrite the expression P= f(Q, D, 52, P,H) in dimensionless form by using Pi- theorem, where P is…

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Q: Prove thut:f focK, 2) Y is a contimans findion then, g=XxX-> YxY 3 3 n K2) = (F(), PU=) Einction is…

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Q: evalnante the folobwing integrationollowing a fferent Path C I'm troid.cpathz pathi Re (3,-2) path3

A: Note:- For part (3) it is not clear that the term written with sint (or coefficient of sint ) is "I"…

Q: Solve using Lapiace transform: P4t - uz = xt, t> 0, u(0, t) = 2, u(x, 0) = 1. = 2, u(x,0) = 1. %3D…

A: Introduction: Apart from solving ordinary differential equation with initial values, partial…

Q: 1. Let F(x, y, z) = (x + y², y + z²,z +x²). Let C be the triangle with vertices (1,0,0), (0,1,0),…

A: by using guass divergence theorem

Q: Exercise 5. Consider the function f(x, y) = sin(xy), 0 ≤ x ≤ 1,0 ≤ y ≤ 1. find local maximum and…

A: Given that: fx,y=sinxy, 0≤x≤π, 0≤y≤1. The objective is to determine: →Local maximum and minimum.…

Q: Exercise 5. Consider the function f(x, y) = sin(xy), 0≤x≤T, 0≤ y ≤ 1. = π, • find local maximum and…

A: Given: fx,y=sinxy To find: Prove the condition

Q: Vector Space [SADT6] If F (x, y, z) = xyzi – ež cos æj+ xy? sikat is V ·(V×F)(1,2, 3) Cos x 1 0 2

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Q: Sketch the dijferential equation de ト(是+Co) dt ) Determine all the equi librium pointls) b) Use…

A: The sketch of the differential equation dθdt=1-2222+cos θ⇒dθdt=12-22cos θ is the following.…

Q: tor field F = 21 + 4j + 3k across the surface S.

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Q: reflection across the х-ахis U A) T(0, –4), U(0, 1), v(1, 1), w(4, –3) C) U(1, 3), v(0, 3), w(-3,…

A: We have to find reflection point

Q: Ques. 3: Check whether the operator T: R2 → R² defined by T(x,y) = (y,x) is linear. Moreover if T is…

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Q: 4)Determine the jacobian u = x (1– r²) i, v= y (1- r²) w = z (1 – r²) /hen r2 = x² + y2 + z2…

A: Given u=x1-r2-1/2, v=y1-r2-1/2 and w=z1-r2-1/2 where r2=x2+y2+z2…

Q: Utt – Uzz = 0 0 0 %3D - u(x, 0) = 1, ut(x,0) = 0 0 < x < T u(0, t) = 0, u(7, t) = 0 t2 0.

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Q: -> Model made the when String wave is up of non-homogeneay Constant. material. String It is qun of X…

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Q: Write the chain rule for- at aw given that w = f(x,y,z); x = g(t), y = h(r,t), z = k(s,t)

A: We are given that w = f(x, y, z), x = g(t), y = h(r, t), and z = k(s, t). We need to write the chain…

Q: Find a non zero unit vecor ôv that is orthogonal to uz= (1,2,1) and Uz= (2,5,4) in R³.

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Q: , t ≥ 0) be standard Brownian Motion Find E(|W14 − W10|) Show that E((W14 − W10)^4) = 48

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Q: carulate the aistance between pointS k=(0,9) and . G7= -6,6) inthe.coordmate Diane. mo0 Cnuer :…

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Q: P. let f-uti and fcz)=z= Prove that U and v Stadify lasplare equation

A: A function f(x,y) satisfies Laplace equation if fxx+fyy=0 Given function is f(z)=z3 Substitute…

Q: az and ди az Q3. Evaluate at given point (u,v), z = 4e*lny, x = Inu cosv, av y = usinv at point(u,v)…

A: We have to find partial derivatives.

Q: Find the linearization L(z, y) of f at the given point. Surface: f(r, y) 6tan '(ary) (2) Point: 2,…

A: To determine the first order (linear ) approximation to f(x,y) at the given point

Q: A point charge, Q=2 µC is located at A (4, 3, 5) in free space. Calculate E,, E4 and Ez at the point…

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Q: Quesnin Find the uGlve av valves ot c that Satisty the esuntion flb)-f ca) in the conclusim t b- a…

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Q: O Find... f+g3= %3D %3D %3D fig=

A: Given,          fx=5x-1 , gx=x+5

Q: u:(x, t) = и (т, Urz(T, t) u,(0, t) = uz(1, t) = 0 u(x,0) = f(x)

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Q: 5. Assume that an ant moves on a plane continuously; that is, its coordinates x(t) and y(t) are…

A: (a) equation of unit circle can be written as - at (0.7,0.1) at (-2,3) we see the change in sign…

Q: Find the Jacobian a(x, y, z) (u, v, w) for the indicated change of variables. If x = f(u, v, w), y=…

A: Find the corresponding derivatives and then find the determinant

Q: When can we apply the Green's Theorem to compute circulation in R^2? O Curve C is simple and closed…

A: Note that Green's theorem works only for the case where C is a simple closed curve.  Further notice…

Q: arametrize the monkey saddle z=x^3−3xy^2 by using u=x,v=y as the parameters.  plot the image

A: Given equation is, z=x3-3xy2 Take u=x,v=y Then the equation becomes, z=u3-3uv2 The counter map is,

Q: use initial conditions u (0, t) = 0 and u (T, t) = 0 u (0, t) = (c1 + c2) (c4 + c3t) = 0 » (c1 + c2)…

A: We have to use the conditions c1+c2c4+c3t=0 and c1+c2e-πc4+c3t=0. We will check whether all the…

Q: evalinaite the folliwing inigratio hi fulliwing dif* PathC I'm f0,1). (3,!) parhz path! Re path3 :|…

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Q: %3D Show that for all 2, a, BE C, A(a + B) = àa + A8 fiold ofE the

A: (2) We have to show that for all λ,α,β∈C, λα+β=λα+λβ Let λ=a1+ib1, α=a2+ib2, β=a3+ib3…

Q: Exercise I f(1, y)yz (a) Let f(r,y) = rỷ - . Then deduce that f(1,y)zy (Clairaut's theorem). %3D

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Q: az and ди az Q3. Evaluate at given point (u,v), z = 4e*lny, x = Inu cosv, dv y = usinv at point(u,v)…

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Q: u:(x, t) = Uzz(x, t) u(0, t) = u(1,t) = 0 u(x,0) = f(x)

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Q: Theorem:For all Xiyiz,w EN i) X<y ^ z sw =)x+Z <ytw ii) xsy ^ zw =) x+Z< y tw )x<う tsw 1 Esw うメ+ と x…

A: Solution: We know that for x,y∈ℕ If x&lt;y then ∃k∈ℤ+,k&gt;0 such that x+k=y If x≤y then ∃k∈ℤ+,…

Q: Ques. 3: Check whether the operator T: R2 → R2 defined by T(x, y) = (y,x) is linear. Moreover if T…

A: A mapping T:R2→R2 is a linear transformation if and only if a) T(u)+T(v) = T(u+v) b) T(cu) = cT(u)…

Q: vVr ITe uruit 10 dEscribe EUCN TraNSTOPmUTON. 本y A 9) A' Z' Z'. K N' K' A n'. K. K' Rule: 12)

A: The given figure AZNK translated into A'Z'N'K'