3. Prove that if a > 1, then a"/n → o.

Q: (a, o) is not measurable.

A: to find that a,∞ is measurable or not  proceed as follows We know that every interval is measurable.…

Q: 3.) Prove (cA)" = cCA) %3D

A: Let A be a m×n matrix so A=(aij)  1≤i≤m and 1≤j≤n ie A has m rows and n columns. By AT we mean…

Q: OShow that in 27 and use Soot method has bisection approximation to the Soot * at leest within a the…

A: The given equation is. fx=x3+4x2-10=0 fx=x3+4x2-10 To find the root in the interval 1,2 that is…

Q: Show tH In k CHint dbtain o formdar for Sn Hint dotau forunlar

A:

Q: Hor what salue of e dois th. a tollowng matrex haue an Tnverse Q. 2. 2.

A:

Q: Prove that I(e) = dr, e> 0.

A:

Q: 3. Use the Racetrack Principle to show that: In x 1

A: The Racetrack Principle :-

Q: 1. Prove that the followingn is a theorem in SD. Av - A

A: Theorem :-

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

A:

Q: Prove for all mEw and n E w, we have that m+ ·n=m・n+n.

A: Given that m,n∈ω. To prove: m+· n=m·n+n

Q: Functional theory and functional analysis

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

Q: of is: If f(z, y, z) = ry z' + In (z) In (y²) In (z³) then dz

A:

Q: Prove by induetion onn that for all irdegers nz2, Nz2,Gilit)

A:

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: Prove H'n(x) = 2nHn−1(x), n = 0, 1, . . .

A:

Q: 81/ show that *if ve(Xジーズ) oif v=(

A:

Q: Q: Prove that tim %3D

A: We have to prove the limit

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

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

Q: U prove that In (l+x)) 2.

A:

Q: az Find if yz – In z = x + y ax 3.

A: We have              yz-lnZ=x+y

Q: =8, d=9 ation u such that (a, b, c, d) = p

A: The value of a, b, c and d are given as follows, a=5, b=13,c=8,d=9. To find the permutation μ, such…

Q: Prove that Z(Sn) = {e} for n ≥ 3.

A:

Q: 1. Condense and expand. a) Condense as a single quantity: 1 In(3)+- In(x? +1)-3 In(1+x) 3 b) Expand:…

A: Given, (a)  To condense ln3 + 13ln(x2+1) -3ln(1+x) (b) To expand lnx2+1x+2(1+x)5

Q: If delta is large according to Cohen's classificantion, then the difference between u1 and u0 is…

A: Given that - If delta is large according to Cohen's classificantion, then the difference between u1…

Q: let X be 4-VV flon)= To Finel ECX) oedECXY)

A: f(x) = x/10 where xx = 1,2,3,4

Q: Verify Eular,s theorem for z =ax2+2hxy+by2

A:

Q: = Prove that E = ehd.

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

Q: Q: Prove that tim x"- a" %3D

A: we have to find the limit of the expression

Q: prove: sE121y |Re(z)+| Imcz)l

A:

Q: Show that if x is in both W and W-, then x = 0.

A: Dot product of perpendicular vectors is 0.

Q: Verify S Tokes' Theorem To 2.

A: Introduction: We know that stoke's theorem is given by the formula, ∮CF.dr=∬s2∇×F·n.dσ

Q: Let x, y, z E Z be such that both odd, and z is even. Prov

A: Introduction: Even and odd numbers are distinguished by the following characteristics: Even Number:…

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: (4). Show that of X~UCO,!) as Y=-n-X)~ txponenkalla),

A: i) Uniform distribution : If X follows Uniform distribution over interval (a, b ) then cumulative…

Q: (a) Prove the following property: (:) - (.".)

A: Hey, since there are more than two questions posted, we will answer the first question. If you want…

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: 12 २ (४) = dt | २स Prove !- \) ২-০০) = २(-०० ) 3D \

A: Given that Qx=12π∫x∞e-t22dtTo prove:1. Q-∞=12. Q-x=1-QxSolution:we know that ∫-∞∞e-x2dx=π       ...…

Q: 3. Prove that: na” u[n] = az (a-z)2

A:

Q: Prove S^2 is simply connected.

A:

Q: 5) Prove that d tanh ) |-x2

A: Prove that  d/dx[tanh-1x] =1/(1-x2)

Q: How do I show this proof?

A: Given that To show that,

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: Prove: le* a. ſ csch x = In - |+c lex+1

A: As per Bartleby guidelines rule I am answering only first question as Both question is not subpart…

Q: Show that if E,=1 a, diverges, then En=1 | |a,| diverges. %3D

A: Given, We want to prove that

Q: Assume C and D are chosen at random from {1,2...,n}. Let pn be the probability that C + D is a…

A: The number of pairs (c,d)  with sum m2 is m2-1 for m2≤n and 2n-m2+1 for n<m2<2n. Hence,…

Q: In Z, let H = <5> and K = <7>. Prove that Z = HK. Does Z = H X K?

A: Given: In Z H=5K=7

Q: Suppose that r, s are integers (possibly different from x, y res that ar + bs = c. Show that there…

A: Introduction: Let us suppose that two integers are a and b, greatest common divisor of these two…

Q: Show that if AT Ay = y for all y in Rn, then AT A = In.

A:

Q: prove the following:

A: Given,           f(x-y, x+y)=2(x2+y2) To prove that,          ∂f(x, y)∂x+∂f(x, y)∂y=2(x+y)

Q: By expanding both sides of the identity (1+ x)"+4 = (1+x)"(1+x)* prove that ("**) - (") + «(,",) +…

A: