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Q: Бxї Zet (x, г) бе space, then Co-countable тебя xis not Тз-брасе

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Q: (x+y)dx + Jx? + y2 dy is an example of homogeneous functic OTRUE O FALSE

A: To determine whether the below differential equation is homogenous or not. x+ydx+x2+y2dy

Q: Find the in ter vals onwhich Fare? (M [ncreasing and dec reaglny W concareuf and concave down and…

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Q: det (NT) is sPace Toflogecu! and T=0U{un}such that 7Show that (N, Cl is compact slase

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Q: let (X; Z) v it piece wise comnected ?

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Q: Let f(x, y) = xcosy- y'e*y. fry at (1,0)is equal to: %3D | -2/3 -2 1

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Q: Let x, y ∈ R. Suppose x^2 +y^2 = 0. Prove that x = 0 and y = 0.

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Q: nners who compete in marathon races are described by the join 0<x, y < 1, f(x, y) = (4xy, 10,…

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Q: let H = {n² |n E z*}, determine whether it is closed under

A: Given : H={n2|n∈Z+}   To Check:  H is closed under binary addition or not

Q: let H = {n² |n e Z*}, determine whether it is closed under

A: Here, we have H=n2| n∈ℤ+. To show the set is closed under binary multiplication. This means we have…

Q: find the denivahon of the Runchon bydsing herules ofditkreohe lhon fee) = 7 %3D +260 .3 2.

A: We need to find the derivative of given function. fx=7x3-8x2-1x+250

Q: Complete the proof that AWXY AYZW. W Y Statement Reason WZ = XY Given 1 2 YZ = WX Given 3 WY WY 4…

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Q: o Show that X2 = {(x, y) E X x X : x<y} is a sublattice of X x X. %3D

A: Given that X is a lattice. To show that X[2]  is a sub lattice of X×X. It is enough to show that,…

Q: Find the Cauchy puincipal value of the following integrad ive (x +1) (x* +2) C2 →メ -R

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Q: Show that(i × j) × j = i × (j × j)Conclude that the Associative Law does not hold for cross…

A: Using the cross products of the unit vectors i,j, k, we obtain

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: Evaluat..f.x.dA. wha.is.the..sgiem.in.the.fiigt. R quandrant..bounded..xy=16. X..8....y.z.. y.e.x...

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Q: Let R = [0, 1] × [0, 1] . Est each with at least six rectan IR 6(x + y) dA 2

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

Q: Find all positive integers x, y, z satisfying x · y · z² = 5xyz. '*

A: Introduction :Given , positive integers x,y,zwe have asked to find the values of x,y,z which…

Q: Let X; ~ X"(1) i= 1,2, . - ·, n and assume they all uidependent are Y = Ź Xi %3D しニ」 ان منتتفينتمنل…

A: Given, Xi~χ12 ,i=1,2,...,n a. Y=∑Xii=1n Therefore, X1+X2+.....+Xn~χn2 above is possible using…

Q: Please Lgent let VizLi = L3) and w=L4o=2) belongs to spaln (rloV2} %3D termine whether w

A: yes this belongs to span of (V1,V2)

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: Let T: R → R' such that T (x, y, z) = (a²z + 4az, y, 36z + az). What is a value of a so that T is…

A: For Surjection of T, Dim{Range(T)} = Dim{Co-domain}

Q: Prove that H(x, y) = (x, –y) provides a conjugacy between x' = (4 })x and Y'= (; 7). X and Y' = 1 -1…

A: Given: X' =11-11XY' =1-111Y To prove: H(x,y) = (x , -y) provides conjugacy between both of the above…

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: and y have density flay)=82y tor Find ECX14) and ECYIX) リフズ7679 %3D

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Q: X Y Z' WXXN W. Y ED O XYZ' + XY + WX'YZ (XYZ)+(X+Y) + WX'YZ F

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Q: Let r, y EN such that y # 0, then y+r#0.

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Q: Let x, y € R" be given. (a) If ||z||||y||=1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1 and ||y||…

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Q: Show that f: R → R defined as f(a) = 3a³- 4 is a one to one %3D iuicuon.

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Q: ; Let x, y ER" be given. (a) lf ||x|| = ||y|| = 1 and x - y = 1, show that x = y. (b) If ||x|| ≤ 1…

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Q: メ~ zCe,52) %3D n-1 ECX; - 2) %3D Find MSECT.) and JustCTs) ?

A: Given      X~Nμ, σ2 T1=S12=∑xi-x¯2n-1   and   T2=S22=∑xi-x¯2n+1

Q: find an antiderivative Fon of the function fox)=5sinX such that FCO)=1.

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

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Q: Let f(z, y, z) = z2 +y? + z²,z = /utv, y = /u – v, and z= uv, Find in terms of u and v.

A: we have to partial derivative with respect to u by using chain rule

Q: prove that two vectur ae orthognal A = x + 4y+32 B =4x+2y-42

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Q: Let f(x,y,z) = zIn(x³ycos(z)), find Z 3x² O In(x3ycos(z)) - ztan(z) 0 2 Y о 3z X af ila

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Q: Let F I2). Evaluate JJaw as z² + y? 0

A: In the given question, the concept of the Divergence Theorem is applied. Divergence Theorem Assume S…

Q: consider the curue desoribed by 2y"-x²_4y vevity that the foint (4-25 les on this o8 wrE andd find…

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Q: Let z, w E C. Show that zw = 0 implies z = 0 or w = 0. %3D

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Q: Jraen fusk hon conespaaday to o d'u z ul) = flx). dx² Find the the egualido for conespoodiang to…

A: Given differential equation is d2udx2+u(x)=f(x)                   (1) boundary conditions are…

Q: b- Let X₁, X2,... X (a) Find a comp (b) Find the UM

A: Solution:   (a):

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: Use Gramer's Rule to Find K,y and Z -y-22 = -8 %3D + 32 = 2 %3D 7X +y+Z = 0

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: Let z = 2 - 3xy?+ x². Zay %3D Zyy

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Q: Prave by indretion ŽKczkt) z on n that for all integens aoenzl, 2.

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