9.19. A relation Ris defined on Z by x Ry if x · y > 0. Prove disprove the following: (a) R is reflexive, (b) Ris symmetric, (c) R is transitive.

Q: 8.0. If x-(x,, X, ...,%)«R', define [xL by Prove that xJkL is a norm on R'. N I|} dns - x]

A: We will solve the first question highlighted in yellow. If you want the second question to be…

Q: 18/156) If the Wronskian W of f and g is te' and if (t) = t, find g(t) %3D

A: Given that gx, y=t2et with ft=tTo find gt

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Q: 11. Let f(x,y)=x²y+y?cosx, find Vf. einiog O lo 03002 oldizaog Ics

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Q: 10. Prove that T, is topologically conjugate to the quadratic map F(z) = 4z(1 - z).

A: Solution of 10. To prove that T2 is topologically conjugate to the quadratic map F4, we have to find…

Q: If the Wronskian of f and g is t cos t - sin t, and if u = f + 3g, v= fg, find the Wronskian of u…

A: It is provided that the Wronskian of f and g is tcost-sint. We need to determine the Wronskian of u,…

Q: 5) Let à = psin(4)ū, + p² Ug Evaluate f Ã. dl given that L is the contour of the following figure.

A: Let A→=ρsinϕu→ρ+ρ2u→ϕ we have to evaluate ∮A→.dl→

Q: 2. Find all volves of tand u x(t,4)=0 and simultomebusly such that =0. 3. 5x-11* C.

A: Get the equations for:  fx=0fy=0 15x2-11y=0-11x+3y2=0 or 15x2=11y3y2=11x

Q: 1 Р ven as If th ● q 2 x are real and positiv llowing relations shc

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Q: 4. i) Let X = B [a, b] and let d be the sup metric on X. If n → x in (X,d) and an is continuous at…

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Q: (8) Show that the map f(z) = 1/z is a bijective holomorphic map from S? to itself, using the charts…

A: Note: A function is holomorphic if it is analytic everywhere except one point. Given: fz=1z, z≠0

Q: 5. Verify that the. functrun.u=1/ xy2? satis fies the threendimensianal.place cop.x+Uyy.+Uzz =o %3!…

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Q: 3. Find all the fixed points and classify cach of them: f(r,u) ryev,

A: Solution:- Fx,y=xye-x2-y2 Put Fx=0 and Fy=0 Fx=e-x2-y2y-2x2=0and Fy=y-2y2 e-x2-y2=0 So,  0,0,12,12,…

Q: 8.F. Ifx= (1, I, --- ,)€R", define x, by e that z- l, is a norm on R'. Prove

A: Given that x=x1,x2,..,xn and x1=x1+x2+...+xn. The objective is to find the whether x1=x1+x2+...+xn…

Q: Let C be the shortest path that connects z to ri and /= J, (sinhz + 1)dz. Then O 1 cosh r+ n(1+) O…

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Q: 3. Show that the function p : F → Ę which maps o to o is a bijection from F to Fe, where and ar to…

A: Let ϕ:F1→F2 be a function such that, ϕ0=0. Also given that ϕαr=β3r, where 0≤r≤6 When r=0,…

Q: See picture below.

A: Consider a function f(x) such that:

Q: Find to the the equation du green funclion corresponding pula)=fex) conditions U(o) =0 with and…

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Q: Let po) - X In (x) , using the following approx im for the secoud denvative fcxo) = FOXO -h)-ZR…

A: Introduction: Apart from differentiating a function analytically, the derivative of a function can…

Q: Find the ared of the reyion R bound ed.by and the liney=x+2 2. 2. =y-yand the line y--x ......

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Q: 1. Given that z = x+ iy, where x, y are real and y #0, express z + 1 in the form a +bi where a and b…

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Q: give an example or prove it doesn't exist j. an orientation on K44 which contains no sources or…

A: The given statement is,  An orientation on k4,4 which contains no sources or sinks but is not…

Q: 1. Show that sinz is unbounded on C and lyl <|sinz] <ebl z=x+yi € C. for

A: Given:         We have to show that sinz is unbounded in ℂ and y≤sinz≤ey   for z=x+yi ∈ℂ Function…

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Q: 3. Use Green's Theorem to evaluate G³ï+xj)•dr around the perimeter of the rectangle 0<x<2,0<y<3.…

A: Given ∫C(y2i+xj).dr We know that dr = dxi+dyj Thus ∫C(y2i+xj).dr = ∫C(y2i+xj).(dxi+dyj)  =…

Q: 2. Consider the function f(z) = ( -3) on (0, 1]. (a) Prove that / for r, ye 0, 1], (b) Prove that /…

A: Contraction mapping theorem: Let (M, d) be a metric space. A mapping f:X→X is contraction mapping,…

Q: 2. Use the Squeeze Theorem to show that f(r) = 2 is in R(0, 3).

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Q: Question # 01. Consder z= {acbos a-b =0; S2 Interpet that eguivale nce relation. ~ 18 is

A: That's easy, just show that this relation is reflexive, symmetric and transitive.

Q: Consider Uu=4uzzy u(x,0) = u(x), u₁(x,0) = u₁(x), on the domain -∞<x<∞, 0≤t<∞o. Suppose that both…

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Q: Which of the following is a nonlinear second order nonhomogenous PDE a. xux-Uxx=tuxt O b.…

A: To find - Which of the following is a nonlinear second order non-homogenous PDE x ux - uxx = t uxt…

Q: Suppose U and v are conformally equivalent. Prove that if U is simply connected, then so is V.…

A: Given that U and V are conformally equivalent that is there exist a mapping f from U to V such that…

Q: - Pcosø prove that dw xy is Cont s Lony) - the fun ction (-1, 2) = x*y+z and x = PSinf cse y=pSi- -…

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Q: If the Wronskian of f and g is t cos t - sin t, and if u = f+ 2g, v = f - g, find the Wronskian of u…

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Q: (c) Evaluate d Gosh: where C: |z| = 2 by using Cauchy's residue theorem.

A: Given integral is ∮C dzcoshz;   C : z=2 As, we know  If z = x+ iy then z =x2+y2 As given that  z=2…

Q: 1 : Determine the manimom and Nalve of the function minimumn x'tyス condition under the *+ 2 7?== 1.

A: To find the absolute maximum and minimum of the function using lagrange multiplier

Q: 3,4 show that the integsal (Xy°ty%dx + 3) Independent of the path joining the peints (1,2)and 3,4).…

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Q: The function u, takes on the following values : 1 1 1 1 1 u, = , u. + .....u, 10 1 + 3+1 + 32 +…

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Q: 5. If u = ee Cos(alogr) prove that a'u 1(ôu 1 a'u = 0 + r ôr

A: Derivative.

Q: Oct 31, 2021, 16:44 Problem-2 0 Let foo = x?-2a and gcauz VI-x 6) is q CG (-Z)) defined! domain ind…

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Q: 2) Suppose S,T E L(V) are such that ST = TS. Prove that null S is invariant under T.

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Q: The curl of f(x,y,z)=xyzj is None of these. хуk-yzi О ху-yzk ООО О

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Q: Compute the value of f.dr If F= -yi+xj and c is a from (-1,1Y to CI,1) %3D SemICirele

A: Proceed as shown below

Q: 3. Show that a reflection a in the x-axis defined by o(x, y) = (x, -y) is an isometry.

A: The solution of given problem is followed by

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Q: 2 - Find the inter val on which f are Con Cave down and infleobion Points a -y = x2 5X+10 6- ソ= (¥+…

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Q: A mapping f:C→ C is called bounded, if sup |f(2)| < o0. zEC Show that sin, cos : C →C are unbounded…

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