Prove that Σ = 2" . a. x=0 b. = 0. x=0

Q: 10 of 17 If y(t)+(t-r)y(r)dr=t, then y(t)= Su-nyndr3Dt,

A: Convolution Theorem: The Laplace Transform of the convolution of f(t) and g(t) is:…

Q: 1. Let U2 = 2. fui, 4.} is an orthonmal basa fo IR Show that

A: The set of vectors v1,v2,…,vn of a vector space V are said to be an orthonormal set of vectors if…

Q: 4. Consider the following figure and proof. R Given: GA || TE Prove: AGRA~ATRE

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Q: If I, = S e cos" xdx, where n > 2, prove that In 1+n(n-1)In-2 n² +1

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

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Q: Consider the Venn diagram below. Illustrate the other De Morgan's law by selecting the region(s)…

A: GivenAc ∪ Bc

Q: 12, GIVEN: JKI KT, ET 1 KT, KV TL, IL EV. PROVE: AJKL AETV. T.

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Q: If I, = [x^tan"x dx, Prove that (n+1), + (n-1),,2 ° п 1 %3D 2 n

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Q: Let (W, t > 0) be standard BM. Show that P(n|w,1 – Wa sc) → as n → 0.

A: From the given information,  (Wt, t≥0) be standard Brownian Motion. Note: In the given situation,…

Q: Prove that on average, permutations of length n have H, cycles, where Hn i=1

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Q: - Justify the last two steps of the proof. Given: RS UT and RT US Prove: ARST AUTS

A: Given that:

Q: メ (myst メート→ Q(2,4) where: Path C くz rom ○)と to over the Evaluate the

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Q: Show that (hcs) de = 1 In 27 e %3D 2. 20 (ite")(2 + 1)

A: To show: ∫0ln 2e2x1+ex2ex+1dx=12ln2720. Concept used: Integration of ∫1vdv is equal to ln v+C.…

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: 2. (– 13 + 3i)31

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Q: dy If then de impossible to calculate O In(æ)

A: 7.  slope of tangent line  slope at point ( 4 ,2 )

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: Show that if A is nonsingular and AB = O for an n × nmatrix B , then B = O .

A: We have given  matrix A is non singular and AB=0 for an n×n matrix  B. We have to prove that B=O

Q: 7) Prove te follo aing theorem 18 A and B ve madrices cof siees such that ore odition is defined…

A: Suppose, A and B are matrices of same size such that,    Where,   Now,…

Q: メ人 xp- Vtan (e) sec?(e) de Evewale Jhe Jollowing! op (e)as (a)

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Q: Prove that on average, permutations of length n have H, cycles, where Σ Hn i=1

A: We will take an arbitrary set containing n elements and observe the required permutations.

Q: Prove that (S ⋂ T)c = Sc ⋃ Tc and  (S  ⋃ T)c = Sc ⋂ Tc .

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Q: 1. In the figure, E is the midpoint of (NS)¯and LSzZN. Which postulate justifies that APES = A MEN?…

A: Introduction: When two parallel lines are intersected by a transversal, the pair of angles formed on…

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: = Prove that E = ehd.

A: We know that Ef(x)=f(x+h)

Q: SHOW that V Ź a? Jor a, E IR when His ineguaity e kold .

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Q: Let SCR. If sup S (resp., inf S) exists, then it is unique. ylgn ihi

A: The supremum (or least upper bound) of a set S ⊆ R which is bounded above is an upper bound b ∈ R of…

Q: 1. In the figure on the right, which postulate proves that ΔTIK ≅ ΔTOK?

A: Given,

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: Use the diagram to prove that ACAS ATAS. A T. Given: CS = ST and mzCAS mzTAS= 90 Prove: ACAS= ATAS

A: Given : CS ≅ STm∠CAS = m∠TAS = 90°

Q: cos (o,+ O>)+ ì s:in (8,+Ə.)) Prove this kW- Mon 183O

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Q: 3. ncnt) use PMI to prove that E

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

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

Q: 2. Find the exact \ength af the following curvis

A: Arc length L=∫ab1+dxdy2dy

Q: 1 1 The identity I = [ |" dixcy=f, S* * dydx is

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Q: if w= /x2 + y2 + z2, x= erCos0, y=erSin0, z=ee prove that aw/ar= e?r/w and aw/ae = e20/w

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Q: Prove: Vn e Z,if n is odd, then 3n+5 is even.

A: Consider the provided question, To prove: if n is odd integer, then 3n + 5 is even. Proof by…

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

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Q: (b) Using Venn Diagram to prove that (A U B)e = A° N B° ?

A: To prove the following using Venn diagram A∪Bc=Ac∩Bc First consider the left hand side  Set A

Q: 5|8" – 3", Vn EN

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Q: Let fELoi Show that i for any E>o, the set 3- S has a positive measure -

A: For f∈L∞ , f∞=infM>0:μx:fx>M=0For M>0, defining the set AfM=X:1 fx>M⇒For f∈L∞,…

Q: Prove that S, pm (x)Pn(x)dx = 0 if m# n ? %3D

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Q: e){x*,x%,x}on(0,)

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Q: Consider a S = {x|x"=1} is S, equals to S?

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Q: Suppose that fo sf,:X-gy and g,-3 YoZ Prove that (Hint : First use ce) to show that gfe g,, and then…

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.