For all n, d e Z where d + 0, d\n * n= dk for some kEZ. Disprove: For all integers a, b, and c, if a|(b+c) then alb or alc. n assume that a # 0, because otherwise we couldn't sau that ol(h e

Q: Prove the following fact: A" = 3"-1A. 1 1 1 1 1 1 1 1 1 A =

A: Given, A =111111111  We have to  prove An = 3n-1A

Q: Compute each of the following. b. (3)* d. (-3). f. (1)** a. (- 10) - (" 10)° C. 50 147 e. g. 4+3 5-2…

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: Evaluate (Vx+ f. d dx. OA. A. Vx2 + 2 + a² - a In + C O B. Vx2 + a² - In |x| C. Vx2 • a? + In- + C…

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Q: Which of the following is not equal to P(100, 2)? 2P100 100! 98! 9900 100P2

A: We have given, P(100,2) The number of permutations of n things taken r at a time is defined as,…

Q: )(2n) for conplex number sequance show that if lm En=1 then 3no fN such that for for Hn 7 no o Znto.…

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Q: Supposer FCE, acE is algebraic F and dog (a/F) 13 odd. Proveo that F(a)= F(a²). over

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Q: sobeit r-9xi+37i+922k and tr=35 here tri- rfindatlof gradffland div where C fixedamonnt

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Q: (64e" — 128)е* de Г (10е" — 8)(— 2еt — 8)

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Q: TRUE OR FALSE  x and y are POSITIVE integers.

A:

Q: Evaluate: L(e* -3t * sinh 7t).

A: Given: Le-3tsinh7t

Q: - 25 -dr (x – 4)(x + 1) Evaluate

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Q: Let →u=⟨6,−4,−6⟩ and →v=⟨−5,−3,−6⟩. Compute the following:

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Q: Evaluate L{t cos 4t} s2 - 4 a) s2 + 4 s2 +4 s2-16 b) s2-4 s2 + 16 c) s2- 16 d) s2 + 16 O a Od

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: (b) Let A¡ = [-i, 1] for every positive integer i. Find U A¡ and N1 Aj.

A: Given that Ai=-i,1 for every positive integer i. That is, A1=-1,1, A2=-2,1, A3=-3,1 and so on. To…

Q: Let F = (, , 2). Calculate div (F) and curl (F). (Use symbolic notation and fractions where needed.)…

A: We have to calculate  and .

Q: . Show that p(X) = XP-1 +... +X +1 when p is prime.

A: For every integer n≥1, the nth cyclotomic polynomial Φn is the monic polynomial whose complex roots…

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Q: V ) and A, p 0, and e0. Show that then I',AF0.

A: In the given question  given that γ l=(φ∨ψ) , ∆,φl=θ and and also ψl=θ then we have to prove that…

Q: If -5n-2, then f(3) is 04 O 55

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Q: dx Sx²+ 4 2. 多.区

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Q: Let n eN 1. Show that o (n²) = ng(n) 2. Show that o (n) +

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Q: 2 Find (5a" + 4a*) da 1

A: We can find the integration value as below

Q: (3c) Let n E Z. Prove that if n is odd, then 4|(n² – 1)

A: here is the proof

Q: Find the dual of the Boolean expression I +1.0+ Fyz O z. (z+1). (7+ y+z) O T. (7 +0). (7 + y+z) O z.…

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Q: n² -1) 2n³ + 1

A: ∑n=1∞ -1nn22n3+1 use the alternating series test an=n22n3+1 an is positive and monotone decreasing…

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A:

Q: If k = (0.0003,-0.0012, 0.0015,-0.0014) in R4 then -5.2||||=0.0062

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Q: Find z-transform for 8 © x(n) = 5ucn) - 2 (055 un) = 5 e(n) - 2 (0-5) u(n)

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Q: 1. Show that 2465 is a Carmichael number.

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Q: Simplify completely: 0 ~/~ 2 (₁ + ²)² - (¹ - 1) ¹)²³ 1 a a

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Q: Osrc> lete he Riemen th four sclbinenals ight entpaints sum for f(r) - ( -r? Osr6> , taking tHe…

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Q: 2,5 Evaluate O 근43 0,0 2,1 7,4 (Z+ €)dz (2+i) dz 7.4

A: As per the guidelines I am only answering the first 3 questions.  Kindly repost the other questions…

Q: leoinov o and 7o iqeng od dw nislqont-( do (0) d o on tud pouso mbrore XE G Such that X? -3X -4=03…

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Q: 1 1 1 2 4' 8' 16 32 ' 64' 128 1 1 1 The sequence {1, } а. converges to negative one. O b. diverges…

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Q: Suppose b1 + *+ bm < n. Prove that b,!bm!< n!.

A: