prove that n E vol(B6)) > II(b: – a;) vol( B jEJ i=1

Q: Complete the following proof. Given: FG FJ, HG = IJ Prove: HF = IF

A: I have provided solution in step2.

Q: OLet @ = (0,1)n Q = {x€ @104 x<1}. Prove that %3D 2) 2000m

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Q: Prove that ||A||1 = maxi<j<n{E#1 laij|}. i=1

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Q: Given: LM NO; ZLMO = ZNOM Prove: LO NM ments Reasons

A: We have to Prove that LO congruent NM

Q: Let X N (u,1) of size n. Obtain UMVUE for M.

A: We will use Lehmann-Scheffe theorem to find the uniformly minimum variance unbiased estimator for μ.

Q: QR MN ZN = ZR QS MP RS Given: NP Prove: R N

A: In △MNP and △QRS QRMN=RSNP=QSMP

Q: a Prove that < 16 – a| for each a, b e R. - V62 + 1 Va? + 1

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Q: We defined NCE) = ZE for ZE Z Ii]. Prove N (Zw) = NLZ) Ncw) for all Z,W E Z6] .

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Q: Prove by mathematical induction that, for all positive integers n, de (e* sin x) = 23"e* sin(x…

A: To Prove →dndxn ex sin x = 212n ex sinx + 14nλBy mathematical induction for all positive integen…

Q: Prove by mathematical induction: For Vn E Z*,7|(232 – 1)

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Q: Q.1 a- Verify Euler's theorem U= x"In(?)

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Q: b) Prove Y)- min (t, Ye, Kg) is a UMVUE of o non

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Q: Use substitutions to waite (In t)at, for seyo (1n ms of と in 0,9 € N, aE IR E IN, a E IR, a#0 where

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Q: Let r = xi + yj + zk and let r = ||r||. Prove that

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Given: - L KL ON OP NP Prove: ZM L = 2O * View

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Q: Let r = ri+ yj + zk and let r = ||r||. Prove that

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Prove that tr(aA + bB) = atr(A) + b tr(B) for any A, B belongs to Mn× n(F).

A: We need to prove that tr(a A + b B) = a tr(A) + b tr(B) for any A, B belongs to Mn×n(F).

Q: Prove by mathematical induction: X n (U-, Y) = U=1(X nY), for V n E Z* – {1} and sets X,Y,,Y2,. Yp-…

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Q: Let TE L(V, W), where V and W are finite-dimensional. Prove that rk(7) rk(7*).

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Q: 19. f' "'In rdr r'In r dr

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Q: OVESTON Prove that A is inveitine if at0 and at b l Gind The pivos 9 A %3D a a

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Q: 7, Prove the fallo aing theorem 18 (of sizes Such that A and B ere madrices siers addition is…

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Q: 1. Prove with the usual notations that: (a) EV = VE = A (b) A +V =- (c) A= SE Apply the suitable…

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

Q: Fiven: LM NO; ZLMO = ZNOM Prove: LO = NM Reasons

A: Given that: LM=NO, ∠LMO=∠NOM

Q: .Use the De Moivre's Formula to show that if z = (cose + isine), then z" + ; ÷= 2cos (n8) and (금) 3…

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Q: Given: LM NO; ZLMO = ZNOM Prove: LO NM

A: Using Side angle side test,

Q: o prove that knVA=| Test the seuence (ConViordív) of (10) an = (^_-) ) an 15 ら 9n: 3ntl 3n-1 (の+ (7)…

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Q: IS T-dist prove o E(T)=0 QvarしT)=て %3D V-2

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Q: 28. Prove by induction that i(i – 1) (n+1)n(n– 1) i=1 holds Vn E N,n 2 1.

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Q: Prove Va e Z, Vb e Z, 3|(a² + b² ) – 3|a ^ 3|b where xy means x divides y, i.e., there exists k e Z,…

A: In this question we use congruence modulo.The following  are useful in this question1) If  3 |…

Q: Prove that (aA + bB)t = aAt + bB t  for any A, B belongs to Mm× n(F) and any a, b belongs to F.

A:

Q: By using Caushy Riucman Prove that? e ae

A: We will use the following result :  Result : Let the function f (z) = u(x, y) + i v(x, y)  be…

Q: Prove that eie ei(0+2K) ,where k = 0,±1, +2,...., = D

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Q: ronskian of the DE : xp(x)y' + 3y = 0 = er² et? et?

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Q: 27 dr = iex+ h where a, b> 0. Prove that

A: Prove that , ∫-∞∞e2xae3x+bdx=2π33a23b13

Q: ), P{|Zn – c| > ɛ} → 0 as n → o. Show that for any b on g, E[g(Z„)] → g(c) as n→o

A: *Answer:

Q: (a) Let r = ri+ yj + zk and let r = ||r||. Prove that - (1) a

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Q: Show that Z, dv=2010 %3D if B= 2) : -1 Śn s3, ISySY,e

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Q: MN 1 NP, QR 1 RP ΔΟRP Given: Prove: ΔΜΝΡ ~ N R P Exercises 17, 18

A: A triangle with two perpendicular lines

Q: Let a = 8 and b = 9. Find m,n E Z such that am+bn =1.

A:

Q: Let BE Cnxn. If z" Bz = 0 for all z E C, then show that B = 0.

A: Given expression is

Q: prove that tr(aA+bB)=atr(A)+btr(B)for any A,B belongs to Mmxn(F)

A: Let A=aij and traceA=trA=∑i=1maii.. Note that, aA+bB=aaij+bbij. Then,…

Q: 123 A=162 3 3 5 9 3 Let Calceelate Ā By Cayley- Hamil ton theorem.

A:

Q: a) Suppose that you wish to prove that ARST = ASRV. Using the reason Identity, name one pair of…

A: Given: We wish to have the triangle RST and triangle RSV to be congruent.

Q: Then show that N(A) = R(AT)+ and N(AT) = R(A)+. %3D 11-1 02-3 -1 1-2 N(A) = N(AT) =

A:

Q: (d) Prove that IJ CINJ. Give an example where 1JÇINJ. (e) Is (ab a e 1,beJ} an ideal in R?

A: ANSWER :

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.