Ex 3.5.1 Let a = 3 .5-7. 13 and b = 2 -* .5.7.11 - 13*. Show that a|b by finding an z such that b = az. ar.

Q: Let S, := (1 - (-1)"/n :n e N). Find inf S, and sup S,.

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Q: 2, Choose give Single digit positive in te gor f them' and the mean me

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Q: EX: Let S.[22] be asubset of IR Si-[-2-4J; S₂ = (-1,0]; S3 - (04]; S4= (1>2] {Si}, is a…

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Q: 2. Show that by using MEAN VALUE THEOREM. u-v n >0 1+v2 3 <tan- < and deduce that 25 ww 4

A: First we have to show that v-u1+v2&lt;tan-1v-tan-1u&lt;v-u1+u2 where 0&lt;u&lt;v. Then we will show…

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

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Q: Compute for the value of tanh (1 – i) Iny + 2.13i In 2 + 2.13i 2 In 5 - 4.25i 2 In v2 + 2.13i

A: To Compute: tanh-11-i Concept: 1. tanh-1z=12ln1+z-ln1-z2. lnz=lnr+iθ+2nπwhere,…

Q: =[12] and U- = -[] Then A2017U is equal to -1 Let A =

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Q: 5. prove thatS" erf (x) dx =o CA

A: ddx(erf(x)) =2 e-x2π   I =∫-aa erf(x) dxI= erf(x) x -∫ ddxerf(x) x dxI = x erf(x) -2π∫ x e-x2 dx-x2…

Q: 3 Find C at any time7 2l/min SIN SIO 6l /min 8 elmin C NI8 100 Pure waley

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Q: Show theit the fenias +- (AtI)(28+1) (P+1)(2p41)(38+1) (uhese a>0, B>0) conveages if B>a amd…

A: Ratio test If we have series ∑ann=1∞ Then we will find the limit l = limn→∞an+1an If l&lt;1 , then…

Q: If A= then A" + nl is equal to

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Q: Show that the series 3. + + 4 To t (-1) Lonverges absolutely.

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Q: I independent, and that o+zz-5 = 7. Based on the provided information, answe owing questions: ind…

A: Since the question has multiple sub parts we will solve the first three sub parts. Please resend the…

Q: Can Thenem a Séauekie loubimoue of at usuo EX i for OR nemeed is coutimons al spae) nomed fix→X(when…

A: Let f:(X,dx)→(Y,dy) be a function continuous at x=x0∈X       if and only iffor any sequence {xn} of…

Q: Suppose, X-Binom(m.0) and 8- Beta (a, B), then E(X) is equals to, b) d) maß aß ma α+ B me Answer B €…

A: Given: X|θ~Binom(m, θ) And θ~Beta(α, β) Formula Used: X~B(n, p) E(X) = np To Find: E(X) = ?

Q: If Z = eax + by F(ax - by); the value of %3D az is + a ду az

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Q: Blank 1 is movement of a side of a preimage parallel to that side with respect to one other fixed…

A: We have to fill the blanks.

Q: 3. Is this sentence consistent? “There is someone who loves exactly those people who do not love…

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Q: Let X ~ N(0, 1). For any € > 0, show that P(|X| > c) ≤ ²c - ??

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

Q: 1.using the diagrom / mateh the stodenento ad reasans tu whe a two-column that DO =WN. prouf Shaning…

A: Given: DW = ON   To prove: DO = WN   Diagram:

Q: Let 1)" Find sup A and inf A. Provide some explanations how you got their values or why they don't…

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Q: for AUB unih AG B inderser for is not unusual.) Then, A+B= B+ A A B= B A A (B+ C) = A B+ A C A+Ø= A…

A: In this question we need to explain about the underlined symbols ∪ ,   ∩  ,   ϕ  .

Q: Σ (X) E(Y), E(XY ) , Coν ( X, Y) , σχ, σχ and ρxΥ.

A: As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted...…

Q: o provethat WE =c? bWex W=tan (x-et) 3 prove hat f xx + Pyy = o whene fetan () 2.

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Q: Suppose, X0- Binom(m,0)and 0~ Beta(a, B), then E(X) is equals to, a) maß b) aß ma c) d) me

A: Given: Suppose,  Xθ~Binom(m,θ) and θ~Beta(α,β)

Q: prove that var (XY) == 0} 03+ 2} · o3+ 13.03

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Q: Give three examples of Bernoulli rv's (other than those in the text). (Select all that apply.) Ox =…

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Q: eb Let A E M₁ (TR) be given If AAt = On HOME JATOT prove that A = On - Does this hold if A EMn (C)?

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Q: Ex: @ write out the expessien R(n=4) jki in full. wuich aue free and which ane dummy indices ?…

A: We write expression of curvature Tensor

Q: Find all values of z such that cosz = 4.

A: We find all values of z such that cos(z)=4

Q: Let p denote 3x E Z such that P(x)" and q denote dx E R such that P(x)". Ğive a simple definition…

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Q: dq + q = 4 cos 2t dt

A: Given that, dqdt+q=4cos2t On comparing with general equation dydx+Py=Q ⇒P=1, Q=4cos2t, dx=dt…

Q: Show for Re(z) > 1 ex – 1 dr = T(z)5(2). et – 1

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Q: If tanh '() = 1- 12/3, then z = %3D In + 종 In O In In

A: As per the question we have to solve the complex equation and find the exact value of the complex…

Q: Which of the following can you not use to prove A CAT S A DOG? 1. CA DO II. ZC ZD III. ZA E ZOo IV.…

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Q: s involves a different way of wor words with the symbols that repr what the hypothesis and what th

A: Introduction: A proposition is the most fundamental building block of logic. It is defined as a…

Q: Which of the following is false? QCZ

A: To show that all the elements of set X are the elements of set B, the subset is used like, X⊂B   1.…

Q: 22 z) dz Evaluate COS 32/65 e^(2z) cos(z/4) + 4/65 e(^2z) sin(z/4) + c 32/65 e^(2z) sin(z/4) + 4/65…

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Q: (a) Verify that Ex = 477, Ey = 86.8, Ex² = 62,029, Ey² = 2028.68, Exy = 11036.6, and r = 0.93853. Ex…

A: a. The provided information is x days y km/100 xy x*x y*y 72 14.7 1058.4 5184 216.09 76 19.5…

Q: 4. Show that In sin 6 d0 = – n 2 by applying the mean-value principle to In |1+ z| for |2| <r < 1,…

A: ∫0π2logsin(θ)dθ=12∫0πlogsinθdθ                         =12∫0π2logsin2θdθ…

Q: 1 Evaluate e" cos 2z z dz COS 4 32/65 e^(2z) cos(z/4) - 4/65 e(^2z) sin(z/4) + c O 32/65 er(2z)…

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

Q: Suppose PRo=62 this means that 38% of observations greater than 62 %3D 80 Select one: O True False

A: Given a statement about P80. We have to choose the statement is true or false.

Q: ke an example at a Noe therian m adu le is not Artini an.( Prove)

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Q: 1. Let x (x,) E l. Find x if 11-- a. x = 2 %3D

A: This is a question of functional analysis in lp space.

Q: Bla) 31 compute measurable

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Q: Find an expression of for y = 2*ev*, Hint: (a*) = a* . (x) · In a

A: We can find the derivative as below

Q: 5. Let TE B(H). Show that (ker T)- = ran T.

A: Given: T∈BH and T† is an adjoint of an operator T. To show: ker T⊥=ranT†

Q: If E and E, are measurable , then (E,UE) is not measurable

A: False.

Q: Ex 6 Show that X -Ca,i) is HOM with y- (1,00) if X and y have the euraal Seibsipace op. af R Hint:…

A: Homeomorphism: Two topological spaces and are said to be homeomorphic if there exists a function…

Q: If θ̂ is a point estimator of θ, prove that MSE(θ̂) = V(θ̂) + (B(θ̂))2

A: We have given that θ̂ is a point estimator of θ. We know that  MSE(θ̂) = E((θ̂ - θ)2 )