Now Considex a fn abarce of set of finctrons f() x€ (-00gt00) such that of d del varieble Oes ox→ I 00. Fox d lhit weight function w(x)= 1, Determ ine 48 folloing operators dde hermition, 4). id p.

Q: Let X (2,3. 4) and de fined metrie on X as d(x, y) = |-y Find open ball B (2.2) = (0) O (2) 0 2.0…

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Q: 7. In A ABC,X is the centroid. A A. If CW = 15, find CX and XW. W B B. If BX = 8, find BY and XY. C.…

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Q: Letr(t) = (t2, 1- t,4t).Calculatethederivativeofr(t) • a(t)att = 2, assumingthata(2) = (1,3,3)…

A: Given that, rt=t2, 1-t, 4t a2=1, 3, 3a'2=-1, 4, 1 Need to evaluate derivative of rt.at

Q: 3. Compute the inner product g (v,w) of v = + x. 2 əx and w = x.-+ 2y. Əx ay' Where the line element…

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Q: The adjoint operator of the operator L(u): d'u ;xE[0, 1] %3D dx2 with boundary conditions u(1)=2…

A: We are given   The boundary conditions at x=1 is given as u(1)=2u(0); u'(1)=u'(0)

Q: Let x = s e and y =t es. Compute the Jacobian

A: Given: x=set and y=tes.

Q: Let g(r, y) = ye-, r(t) = In(t² + 1), and y(t) = vt. Find g(r(t), y(t)).

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let the function f is defined on the disk x² + y? < 1, then f has a critical point somewhere on this…

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Q: Let M be an elliptic paraboloid z = y² + 2?. (A) "Compute the Gauss map and the shape operator. (B)…

A: Answer for sub question a: Given x=y2+z2 A parametrization is given by: Xu,v=u2+v2,u,v Then,…

Q: Find a piecewise smooth parametrization of the path C. (ti + tj 0 ≤t≤ 1 r(t) = 1 y 1 ≤t≤2 [y=√x (1,…

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Q: Compute the Wronskian of the following equation. y" – 4y' + 4y = xe2x %3D

A: Given: y''-4y'+4y = xe2x

Q: find the Lineartransfromation T:Manz (R)R whose matrit Mp --

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Q: Find a function u = u(x, t) that satisfies the PDE Uxx = 0, subject to the boundary conditions 0 0,…

A: Consider the given differential equation, uxx=0, 0&lt;x&lt;1, t&gt;0 The auxiliary equation of the…

Q: Let X ={li2,3,4,53 Determime the tnith valve Of each of the pioparitons. %3D a) (bx EX)x + x? <3Q t.

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Q: F(X)=JX F: [o,2]-> show i fis lipschit z funcla or not find k to

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Q: If z = f(u) + g(u), where u = = and v = x · y. Prove that x · Zx – y · Zy = y² ·Zyy – x².Zxx using…

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Q: let w- f(xy) and y in Poluy Cordeinate then a+yS %3D or or or 7.

A: Given that, w=fx, y And x and y is in polar form that is, x=rcosθy=rsinθ

Q: Suppose F (x, y) = (2xe-", 2y – a²e="} (a) Find a scalar function f (x, y) such that F = Vf (b) Use…

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Q: Evaluate | CurlF nds F(x,v,z) = - yzi + xzj – xyk, and S is that part of the cylinder 4= x² + y²…

A: Given function is  Fx,y,z=yzi+xzj-xyk To evaluate ∬SCurlF·nds where S is the part of the cylinder…

Q: Let X,Y,T be dotined poinds. Show that if Te X Ÿ then XY = %3D

A: It is given that on considering that let X,Y,T be the distinct points The objective is to show that…

Q: show that fGx) = C,ex +C,e* s a solution to y for all real conatanto C, +C2, and then find C,, C,…

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Q: Let A: C [0,1]→C [0,1]. Prove that operator A is continuous reversible, find A!, 2.11. Ax(1) = x(1)…

A: We have given operator A such that A: C[0,1]-C[0,1].Also we must know that the inverse operator…

Q: Let C: |z – i| = 4 and I = §. -3z2-3 dz. Then %3D z2-1 O I=0 (without applying Cauchy-Goursat…

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Q: Wyx %3D If w = e* + x In y + y In x prove that Wgy

A: Consider a multivariable function . Then the derivative of the function with respect to x is the…

Q: Let x, y ∈ R. Suppose x2 + y2 = 0. Prove that x = 0 and y = 0.

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Q: Let D be the portion of z 2z + 5y inside z+ y 1, oriented up, and let F= (y, z, z).Compute F dr

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Q: Let D be the portion of z =2x+5y inside x2 + y2 = 1, oriented up, and let F = yi + zj – xk. Compute…

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Q: Evaluate || F-n dS where S is the cylinder (including the disk on the bottom) x² + y² =1 for 0<z<1…

A: First, we plot the given surfaces.Cylinder : x2+y2=1; 0≤z≤1Paraboloid : 3x2+3y2+z = 4; 1≤z≤4.

Q: Let W(t) be Brownian motion. Using Ito's lemma evaluate | (4w (t) – 124W (t))dW(t)

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: of the b) nd y- Fons c) with point.

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Q: Let A: C [0,1]→C [0,1]. Prove that operator A is continuous reversible, find A. Ax() = x() + ja-m}xt…

A: Solution:- We have given operator A such that A: C[0,1]- C[0, 1] Also we must know that the inverse…

Q: Suppose {V1, V2}is an orthonormal set. Let w = 301 – 252 and z = 201 + 02. %3D Find w· Z, the dot…

A: v1,v2 is an orthonormal set.w=3v1-2v2 and z=2v1+v2

Q: Let w = x dz ^ dx + (y³ + æ³ ) dx A dy be a two-form on R³. Determine the one-form *d(tw), where *…

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Q: 2. Let i = y?x + xŷ + z²ż, and let S be the paraboloid z = x2 + y? with 0 < z < 1. Show that fci. de…

A: Given  v→=y2x^+xy^+z2z^ and S be the paraboloid defined by  z=x2+y2      , 0≤z≤1 The boundary C of…

Q: Express dw/ar and aw/as as functions of r and s using chain rule w = In(x² + y² + z²), x = re sin r,…

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Q: Let d: R2 x R2 R be defined as follows. d((x1, y1). (x2, y2)) = 3/(x1 - x2)² + (y1 - Y2)². %3D Then…

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Q: Thelem:-TP PTR har ociva bveof %eI,theu f is Coutivlalse- at Xo CTs thecouvese of thevem triue?why?

A: Questions from continuity and differentiability

Q: 3.2. let f(x) = 2, x+4 xez, * 1 - 1 1/2/20 -74x45 -*>$ Approximate the foldoy using Trapezoid mule…

A: In order to approximate the integral: ∫abydx, the trapezoidal rule uses the formula:…

Q: Suppose F(x, y) = (2 + 5y, 6z – 5y²). Use Green's Theorem to calculate the circulation of F around…

A: Given : vector field F→x, y=x2+5y, 6x-5y2 and triangle C oriented counter-clockwise with vertices…

Q: QV A/ Find at (t-) as a funetion of t, if (x = t).(y= vE)

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Q: Let D be the portion of z = 2z + 5y inside z² + y² = 1, oriented up, and let F = (y, z, -z). Compute…

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Q: Use Green's Theorem to evaluate S. axy dy + cxy dy, where C is a counterclockwise oriented…

A: Given : a=2, c=8 We have to use Green's Theorem to evaluate            ∫C axy dy+cxy dy where C is a…

Q: D.Prove that y y(2)= U12,9)+ jve (2,4) anelyli the loplale's as z, than Guetion u and v Satiglics

A: Consider an analytic function f(z) of the form . Then f(z) will satisfy the Cauchy-Reimann equation…

Q: Let A= R- {o,}. det G = {4, t, qf where 1: A> A defined by icx)> x z¢A L+ ズ-A fex) = 1ーメ+x-A 1-X 9:A…

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Q: Evaluate / (7xi – zk) · ndA over the sphere S : x² + y² + z² = | S a) by divergence theorem, (b)…

A: a) By divergence theorem, ∬SA. ndA=∫∫∫V∇.A dV Now,  ∇.A=∂7x∂x+∂0∂y+∂-z∂z=7-1=6 By changing to…

Q: Let C = C₁ U C2 U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line segment…

A: a. Suppose,  F=∇fF=∂f∂x,∂f∂y So, ∂f∂x=12x+2+tan-1y∂f∂y=x1+y2+3y2 Now, ∂f∂x=12x+2+tan-1y Integrate…