For all n E N, let An = {0, 2n, 4n, 6n, . . {x € Z|(3n E NU{0})(x = 2n)}. (a) Find (with proof) [U An. nEN (b) Find (with proof) N An. nEN

Q: 13.Show that the third-order Adams-Moulton formula is yn+1=yn+h12(5fn+1+8fn−fn−1).

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Q: Property 9. If u, exists, then µ' exists for all '13 s <r. Mathematically, if E (X") exists, then E…

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Q: 16-17. Find the value of n that makes AFED~ AZYX when DE = 4, EF = 5, XY = 4(n + 1), YZ = 7n – 1,…

A: To find the value on n so that two given triangles becomes similar.

Q: 4.) Find the value(s) of k such that A is singular. 1 k 2 A = -2 -k 3 1 -4

A: The given matrix is                               A=  1  k    2-2  0 -k   3  1 -4 We have to find…

Q: 19. Let f(x) = e*. Then, for all n, %3D f(n) (x) = e* and f(n)(0) = 1 It follows that T„(x) = 1+…

A: We have given;

Q: 19. Let a, = (-1)" Vn 2 1. Calculate the value of an+1 - a, for odd values of n. %3D А. -1 В. -2 С.…

A: As this is a multiple question type, according to Bartleby Answer Rule, only 1st question is to be…

Q: 1. Aşağıda verilen serilerin yakınsaklık ya da ıraksaklığını belirleyiniz (Yöntemleri açıklayınız).…

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Q: A. let w-e te Find W2

A: We can solve this using u/v rule

Q: 1. Prove That E (ri + si) a; = E}-1ri a; + £?=1 Sį a¿ 2. Find E(-1)k+1 (2k) k=1 3. Given X = 2, 4,…

A: 1)  LHS=∑i=1n ri+si ai          = r1+s1 a1+ r2+s2 a2 + ..................+ rn+sn an          =…

Q: Let n e N, s > 0, a > 1. Show that n! 1"e" dr sn+1 Inz dr 1 (a – 1)2

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Q: dn-1 for all n E Z with n > 2. Prove that for a 2. Let d = 2, and d, neN, d, =. %3D %3D %3D

A: Mathematical Induction is a special way of proving things. It has only 3 steps: Step 1: Show it is…

Q: If z + In(e 2 – e" + e*) = 0 -2x az find at the point (0, 0) O-3 O 3 O-2 O 2

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Q: If z' + In(e el + e²) = 0 dz find ar at the point (0, 0) O 3 0 -3 O 2 O-2 « Previous

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Q: Let X1, X2, . ,X, be ar.s.of size n from N(0, 01). find the m. l. e 01 and the corresponding M. L. E…

A: # given X1,X1,...xn from normal(theta1,theta1)  Then to find mle of theta1

Q: If xn → 0, then for every e > 0 there exists N e N such that n > N implies xn 0 there exists N € N…

A: Hey, since there are multiple sub parts posted, we will answer first three sub parts. If you want…

Q: Construct the fundamertal soluton G(x, E) -?G= S(x- E) X, E ER? with, as x -E00 or

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Q: Let X₁, X2, ..., Xn be a r. s. of size n from N(0₁,0₁). find the m. l. e 0₁ and the corresponding M.…

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Q: Given: e || m Z3 = 24 1 Prove: e || n m 3 4

A: Given that, Here t is the transversal and∠3≅∠4

Q: 4. Work either (a) or (b), NOT BOTH (a) Let In = for n E N. Prove that nIn = 0. 0, n n%=D1

A: a. Given that    In=0,1n  for  n∈ℕ. And we have to prove that…

Q: Suppose X and Y are two independent and identically distributed geometric random rariables. The pmd…

A: PMF of X is given by, P(X=x) = p(1-p)x-1 , x=1,2,3.... Now,  ⇒P(X≥x)= ∑t=x∞ P(X=t)= ∑t=x∞p(1-p)t-1 =…

Q: What can you say about the upper bound of E(x) for numbers of the form 3^(2n) + 1?

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Q: 1. Let X~Poisson(a). Show that E[X(X – 1)(X – 2) ... (X – k)] = ak+1 -

A: Solution

Q: If z + In(e3* - e + e²) = 0 dz find at the point (0, 0) -3 -2 3. 2.

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Q: Property 9. If u,' exists, then µ' exists for all 1 <s<r. Mathematically, if E (X") exists, then E…

A:

Q: The Wronskian of the given function (e2*, e*/2 ) is

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Q: The Wronskian 1. Show that the functions e", cos x and sin x are linearly independent. 2. Show that…

A: 1. The functions ex, cos x and sin x are linearly independent.2. The functions 1, sin2x and cos2x…

Q: The largest interval for which the IVP: (In(e* – e)) y' + y = 1, y(5) = 0 %3D X-6 has a unique…

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Q: 1. The function x(t) = el5t periodic signal but, function x(t) = e5t aperiodic signal.

A: Periodic and aperiodic signal

Q: If e'z = /3 -i.Then Im (z) is %3D O a. e2 b. 0 С. 1 d. -In(2)

A: eiz=3-i Now let z=x+iy. Then, ⇒eix+iy=3-i⇒eix+i2y=3-i⇒eix-y=3-i…

Q: Σ (-1)" Given: sin x = .2n+1 for x E R (2n + 1)! n=0 (-1)"(2n + 1) 4" (2n + 1)! Compute the exact…

A: Sum of the series, using Taylor series expansion

Q: 2 Let xk = E(k+1)(k+2) for all k e N and define S, = Ek=1 ®k• (a) Evaluate Sn as a function of n.

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Q: 98 unfornly distributed the death cre CHX+h) then nen 2n+n M Prove t 2+h pmx

A: If the deaths re uniformly distributed in the interval (x,x+n) Then  qnn=2n*Mxn2+n*Mxn suppose qnn…

Q: 1/n ( e) E- (In n) VIn² n– 1 n-3 (f) E(-191 \n+1 n=1 n+1 ( g) š(-100)" n! n=1 1 (h) E: 'n(1+In² n)…

A: The nth partial sum of a seriesS=∑1∞an is defined as Sn=∑1nan. The series is convergent, if the…

Q: (17) Define S(n) as follows: n S(n) : i(i!) = (n+ 1)! – 1 i=1 Prove Vn e N1, S(n).

A: Consider the given expression. Sn=∑i=1nii!=n+1!-1 Now, use the mathematical indication to prove the…

Q: | [5æ-+3 e + 9ª – 7] dæ 5x-1 Evaluate : o ln(x)³ + e3* + 9° ln(9) – 7x + C, Where C is the parameter…

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Q: Let X1, X2,..., X, be i.i.d N(0, 1). e most powerful test for testing H : 0 = 0 against K > 0. ower…

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

Q: () 2k = 3", Vn E N k k=0 k n+1 Σ 2 Vn E N, n > 1 3 k=2 į * () 主) n 3k = 4", Vn E N %3D k k=0 = 2"-1,…

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

Q: n2 for all n E N. 4n Let r, :=

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Q: Find L{{t"+3)*} O none of the choices given n! sn+1 n! 2. +6 S2n+1 n! 6. sh+1 (2n)! n! s2n+1 +6 sn+1…

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Q: (-1)" p2n+1 (2n+1)! Given: sin x for x E R n=0 (-1)"(2n + 1) 4" (2n + 1)! Compute the exact value of…

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Q: Formally prove the T(n) = (5n – 4)° is O(n³). Show all work and all steps to receive full credit.

A: Order: T(n)=(5n-4)3 T(n)=(5n)3-3.(5n)2.4+3.(5n).(4)2-(4)3T(n)=125n3-300n2+240n-64

Q: * 3. In each case, determine if the statement is true or false. (a) For all [a] e Z6, if la] [0],…

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Q: 8. Let 2ni S7 = e7 = cos- 27 + isin- 7 7 a. Prove that E¢ = 0 k=0

A: we have ζ7=e2πi7=cos2π7+isin2π7we have to prove…

Q: (e) Choose {X,}"-1 from [0, 1]. Let p, be the probability that X; + X;+1 < 1 for all i € {1,2, ., n…

A: Given thatXi for i = 1,2,3,...,n are distributed uniformly from 0,1. Let us consider two random…

Q: The population P (in thousands) of a country can be modeled by P = −14.73t2 + 786.5t + 117,216 where…

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Q: Let X1, X2, .. ,X, be ar.s.of size n from N(0, 01). find the m. l. e 01 and the corresponding M. L.…

A: # random variable x follow normal distribution (theta1,theta1)  then to find mle of theta1??

Q: Evaluate O |x + 1/² |x - 21³ O 3 ln x²-x2 + C In In In O In x+7 x²-x-2 ·S B +C |x+2/8/3 |x-1|5/3 |x…

A: This question can be solved using the concept of partial fraction.

Q: 14. Substituting appropriate values for x and y into the formula of Theorem 9, show that (a) = 2";…

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Q: Simplification of In x + In(x + 1) = 0 is x² + x – 1 = 0; x > 0 O x² + x +1 = 0; x > 0 O x? + x-e =…

A: