13. Prove E-1(4i – 3) = n(2n – 1) for natural numbers n > 1 %3D

Q: 2. Let {N(t),t 2 0} be a renewal process and (X,,X,, X,.-be the corresponding interarrival times.…

A: A renewal process is a stochastic model that occurs at random and is temporal based. The process…

Q: f(x) * a = 49 (2n – 1)! 2". 72n + 1 + (x – 49)" n = 1 1 ㅇ윽+>m.72n+ 1.n! 1 (x - 49)" n = 0 1 1:3.5.…

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Q: Select one: 2s2 - 2s 6 S-3 O None of these 252 2s + 6 3 3s2 - 3s + 6 2 3s2 3s 6 S-2 Which of the…

A: Topic:- function  Note :- as per our guideline if more than one question uploaded than only first…

Q: 1. Calculate the value of x, y and z. (Use Jacobi Iteration) • 5x- 2y + 3z = -1 -3x + 9y + z = 2 2x…

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Q: Let n E N*. a. Let a > 0. Then 1 as n 0o. b. - 0 as n → ∞ n16/5+2 c. (-1)"+1"" → 0 as n → 0 d.…

A: We know that limx→∞1x=0. It implies that if x→∞, then 1x→0. We need to calculate the limit for every…

Q: 1. Show that, if x(t) and x[n] are even, then x(t) = 2 x(t) dt and > x[n] = x[0] + 2 x[n]. n=-k n=1

A: If a function f(x) is an even function then f(-x)=f(x). Since x(t) , x[n] are even functions…

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: (11) Let X = n(µ,4) and Var(2x) = E(4– 7x) find u.

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Q: 23 4- [fe** dycdx ans :(e' - e' )(e² – e') 12

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Q: (-1)" Σ Given: sin = x²n+1 for x E R (2n + 1)! n=0 (-1)"(2n + 1) 4" (2n + 1)! Compute the exact…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

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: 4. y= 5e, y-s+ax-3x between x-0 and x=1 about y= -3

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Q: Find the first term of: E (-1)n+1 (z+1)" n=1 3D1 O (z+1)^2]/2 Z+1 -(z+1) no solution

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Q: п-1 k n-2 n-1 n-2 () x6n-10 = p %3D k - 4 X6n-9 = 4 n-1 n-1 n-1 k n-1 X6n-8 = h X'6n-7 = P k n-1 n-1…

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Q: 1 О. 15 Show that %3D (D - Q) k e k

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Q: Suppose that the initial population of deer in a state is 5,000 and is growing 6% each year. Which…

A: Formula used of compound interest  A = p(1+r/n)^(nt) where A is total amount after interest  r is…

Q: b) S. 1 /2n+1 n=1 In+1 c) S̟ =E: In° +1 n=1

A: 7) a) The given series to test is S∞=∑n=1∞e-nn. We can use the integral test for checking the…

Q: Prove that L ={(1Z*)"10" | n e N}is not regular.

A: The given language: Then, the above language can be rewritten as, To prove that L is not regular.…

Q: 1) Evalúe a) csch (In 3) b) cosh (0)

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Q: For all x E R, e* = Ln=0 +0+ n! Express f (x) = x e* as a power series.

A: We have to expressf(x)=x2ex of a power series

Q: 2. Define Ej where the reactor rise time of the first batch is less than 55 min. and E2 where the…

A: Given: E1=The reactor rise time of the first batch (t<55)E2=The reactor rise time of the second…

Q: nx) in the E 2n is

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Q: For any n large enough, prove E" ) – = 0(1). k=0

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Q: 1. Expand x³y²(x + y)12. E15.(15) xn+3y15-n ,15-п а. n 12 b. Eo () xn+3y14–n ELo (5) xn+3y14-n С.…

A: From the given information. The given expression is .

Q: Find L {(2 t" – 3) (t +2)} O 2(2n)! n! + s2n+1 6 sn+1 2 (n²!) n! n² +1 sn+1 O 4 n! n! + s2n+1 8n+1 O…

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Q: 00 n + 1 is divergent. If we multiply any constant (labeled as h)to the n + 1 such that n + 2 n=1 n…

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Q: Show that 100 1 arctan(100) – arctan(2) + E s arctan(100) – arctan(2) + 1+ 1002 1+ k2 k=2 1+ 22

A: To show that: arctan100−arctan2+11002≤∑k=210011+k2≤arctan100−arctan2+122

Q: Find g' (3) . g(x) : In(1+t) dt O In(10) O 6ln(10) O In(4) O 3

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Q: Find the radius of convergence and interval of convergence of  Σ 1 to infinity…

A: Given

Q: 4. Compute the exact value of (-1)"(n+2) xn+1 Ln=0 2n+1 (nt1) 100

A: The geometric series formula is ∑n=0∞rn=11-r, where r<1. Break the numerator of the given…

Q: 2. Multi-Step Series E sin(n) n2 а. b. E sin(n) n=1 n² – 5 n=1 -

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 5.6) Apply the integral test to the series 1+e2n n=2

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Q: (-3)"r" ice of the power series Vn +1 n=1

A: Series

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: 10:29 ll LTE O True or False 11. If two figures are congruent there is always just one way to…

A: Statement is given  We have to define it is true or not

Q: 4. Exercise §3.4 #47. Let n €Z with n> 0. Prove that E - a(n)

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Q: Find S ³+1 ln ||+C In In | +C √²+1 None of the Above In||+C

A: We know, ∫dx/x= ln|x| ln|a| - ln|b|= ln|a/b| n*ln|a|=ln|an|

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: L %3D e2t e-3s-6 (s+2)? O e6-3s ( 1 3 + S+2 (s+2)2 O e-3s (s+2)2 1 3 s+2 O e2-3* ( +) 1 (s+2)2 s+2 O…

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Q: {In(8n+1) – In(4n +5)} 20. b. 0 c. In(2) d. In(5) e. Divergent а. 2 с.

A: ln8n+1-ln4n+5 Now, limn→∞ln8n+1-ln4n+5=limn→∞ln8n+14n+5…

Q: The Legendre’s differential equation is  (1 − x2)y'' − 2xy' + l(l + 1)y = 0, where l is a constant,…

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Q: (-1) nt 2 xh l 1+2) 드 he (-1)" (n+ 2 2n+1(n +1 e exact value of )' n=0

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Q: x is within 5 units of 1. Olx-1 s5 |x - 1|> 5 |x -1|2 5 Olx-11-5

A: We will solve the problem

Q: Apply Heaviside's expansion formula to 3s +1 (s− 1)(s²+1)

A: Here we have to find the Laplace inverse of 3s+1(s-1)(s2+1) i.e. L-1[3s+1(s-1)(s2+1)] by applying…

Q: Find the radius of convergence and interval of convergence of  Σ 1 to infinity…

A: Find the radius of convergence and interval of convergence of given infinite series.

Q: 6. Given that -뿔 (금) (규 R(x) 4! 1+. for x E (-, 3), where & is between x and 0, find an upper bound…

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Q: If z3 + In(e 2 -2 e+e) = 0 az find at the point (0,0) O -3 0 3 О-2 O 2

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Q: 7. E(-1)"- Vn +1 n=1

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Q: n +1 5n An bn n + 2' 4n2 – 3' { 400/n -1/(400n2) n even { Į 7 n/(1+n²) 1 901 п оdd Cn dn

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