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Q: - 21 , Prove that + (n? m' ) yn=o 2.

A: According to the Leibnitz theorem, dndxn(uv)=C0nunv0+C1nun-1v1+C2nun-2v2+... Formulae used:…

Q: 1nnd the x-iner and yitro tn caumon. Then gopn we conon uing grapining poper snon Oution

A: Note: We'll answer the first question. Since the exact one hasn't specified. Please re-submit the…

Q: Given that en 2= V and en 3=W,express each of the fallowing in terms of vand w a) in zv0/3

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Q: * If Iz| = Re(z), then z is

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Q: Suppose RC 1. prove that if B has a sup b, then A(U(B))

A: Given:- Suppose B⊂A and to be proved if B has a Sup b, then λ(ϑ(B))∩ϑ(B)=b

Q: 2. fow く2 <a 30 20 Prove thot 大2 %3D n 21

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Q: Disprove the following by countererample and please provide justification for each line of proof.…

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Q: - check the exi's tence of limol of the Lunetiom 41n at X= 1 %3D 2X+/ こ Xラ-3

A: To check: The existence of the limit of the function. Given: The function is fx=2x+1     -1≤x≤1x22-3…

Q: Q: Show if that IÃ+Bl= BI then Rand perpendicula are

A: Given: The sum and difference of two vectors are same in magnitude. A→+B→=A→-B→ Squaring on both…

Q: (4b) Is Tâ onto? How do we know?

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Q: Functional theory and functional analysis

A: According to the given information it is required to prove that:

Q: 15) o veclovs ú = Givetw and Tñ=211 deternine the projection d on 2.

A: This question can be solved using the projection formula.

Q: Consider a robot arm as given in the following figure

A: answer is in next step

Q: Prove that %3D 3 and hence. deduce that. 3--(n+3)Jn43+ (n+s)Jnes to 2.

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Q: .1כ If n33, еxpand u %3D а'хх, a" x,x;

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Q: 11. Let SC R and suppose that s := sup S belongs to S. If u ¢ S, show that sup(SU {u}) = supfs*, 4).

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Q: 4. If X and Y are independent RVs, then O2+ ,(@) = ¢,(@) × ¢,(@)

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Q: 2) of Ec, 4" is convngend can we conclude that coch of these are comvergent: (4)

A: Given The sires is convergent then,

Q: Prove CPA CCQUR)Ve). A SA (CRval

A: Given: The statement is  To prove: The given statement P∧Q∨R∨Q∧S∧R∨Q∧P using truth tale. Formula…

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: Consider o Con Assume He holding holding Vo =Vi =d, thatis, to the ofter going 1. Draw the Pre

A: Hi, there! As per the norms, we are allowed to solve single question at a time when multiple…

Q: 7) Assume dim V = n, dim U = k, dim W = n - k, and U + W = V. Prove that Un W = {0} and V = U OW.

A: Given, dim V=n, dim U=k. dim W=n-k, and U+W=V.To prove that  U∩W=0 and  V=U⊕W.

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: Suppose a tair Coin is flipped twice, het A, = "Head on 1st Toss" A= "Hend on 2 Toss" Ag=" %3D 1)…

A: Suppose a fair coin is flipped twice, let A1=”Head on 1st toss”, A2=”Head on 2nd toss” and A3=…

Q: A, Az, An are independert,2) PLiln)=r9)-1), where Bi is eitler Ai or Ai for izlityn in please proof…

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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: 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: 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: Prove that Z(D,) # {1} if and only if 2|n (hint: if 2|n look at ri).

A: Let us suppose, Dn=e,r,r2,..,n-1,f,rf,..,rn-1f and nis divided  by 2. Then, n2 is a integer. We see…

Q: v. Let Ac S, prove that P(Ā) = 1- P(A)

A: Given that

Q: -Calculate the Four ier Serie for, fuay =0, -2saso %3D 2 n, Ond plat the fe-

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Q: Prove that (A = B) where (A = ax + ay + az) and (B = bx + by + bz)?

A: Given- A=ax+ay+az and B=bx+by+bz To Prove- That A=B

Q: Prove for all o, TE Sn that oro-1 € An. TTO

A: Permutation

Q: ve that the are lengh - loj secx from

A: Introduction: The formula for the arc length for the curve y=f(x) from a to b is given by,…

Q: Show that U. AS cuhere N= {3 unaluralnun %3D

A: To proveG={N,*} is not a group under binary operation a*b=ab where a,b∈N

Q: Let X, , X>, . X, be a vandam of size I For o hormol distribuien with unrur M and $6. IS 5 Xi = 132…

A: Provided information is ;  sample size(n) = 11 ∑i=1nxi  = 132 ∑i=1n(xi-x¯)2 =99 confidence interval…

Q: show that whe ther RERiemman L-,1} yot

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Q: Let X= Ucy) out of standard er dere d unierm and Y= Uc5) out of

A: From the given information, X=U(4) out of 8 standard ordered uniform and Y=U(5) out of 8 standard…

Q: By using Cauchy Residle Theorem 到一2p 121=1

A: First we have to find residue at singular points.

Q: 5|8" – 3", Vn EN

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Q: Prove that azdə † czbz and dib dzbz

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Q: Compute Simits If they the eist 8+iz z²+4 hit Zマ-2 Re 2

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Q: Let S = {(x, y) :x² + (y – 1)² < 1} U {(3,0)}. %3D Is the origin an extreme point of conv S? Is the…

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Q: Let flr) - ea Than S() -

A: Given: f(x)=1x2+18. So,         f'(x)=1x2+18'        =-8x2+19x2+1'        =-8x2+19· 2x…

Q: If x=sect and Y ztan t, evaluete at 1of the Following to %3D イット

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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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