4|5" – 1, Vn e N

Q: Let S = {:n e N}. a) Show that inf S exists Question 16 %3D b) Show that inf S = 0

A: PART A The given set is : S=1n:n∈ℕ As we know that : ℕ=1,2,3,4,......... The set is given by :…

Q: Which of the following is false? O ("2) = 2(") k ㅇ ") %3 (4") + (F) k n(n+1) (":"): 2 2 O ()² = (?)…

A: We have to check whether given statement is true or false.

Q: "I INAICATE If THtE fOLLUWINh SRRZES ConveilCE OR DeveRしe。エ0ENTICY Tésrs Uszo. TESTS HT in (4nt -n)…

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Q: 14. Consider that * Sof (x)dx = 2 and f'(1) = 3. Find Soxf"(x)dx. %3D 3 O 5 O 1 O 4 O 2

A: We have to find

Q: 70 mily dit butel canden veridde with medn e) =9 let X be a =D4 and stard devr icoen co) =z,±f EMI…

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Q: eferaine the radiea) of the constint e for whichiscentinuos on Eo, 00) if n<a 2n +4,if Y2

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Q: Q1) prove the following below i). Corr(X , Y ) ∈ [−, 1, 1] ii) E(X|Y) = E(X) or E(Y|X) = E(Y) ⇒…

A: We need to use the concepts of Variance, Covariance and Expectations to solve given question.

Q: If k> 0 such that O St the above 4* dx = 3 then k = 2ln 2

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Q: Let fr)-ll for x0, then/(x) is Selact one A-1 * CNone of these DNot defined E1 a.

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Q: : Answer the following 1- Let s = = {+:n € N}. Find max(s), min(s), sup(s), inf(s).

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Q: Consider the following conditions. X = 39.46 O = 5.83 n = 65 Test the hypothesis that Họ: H = 42…

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Q: Part 1 of 5 (a) When a = 0.10 and n= 22, Xieft 11.591 = 32.671 Kright Part: 1/5 Part 2 of 5 (b) When…

A: a)GIvenα=0.10n=22

Q: 9. Prove L'S 25+1 Cs+2)?(S-1)2. %3D

A: Consider F(s) = 2s+1(s+2)2(s-1)2                            (1) Let 2s+1(s+2)2(s-1)2 =…

Q: 7. If [G: H] = 2, prove that gH = Hg (18 from 6.5)

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Q: 3. Prove the Archimedean Property, if x ER. then there exists K E N such that r SK.

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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: Complete the proof by supplying the reasons. 8. Given: LA || SN, LR = NR Statements Reasons Prove:…

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Q: .3 T Evaluate In In e²+j²4

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Q: () 1 1. 3 + In 10 Determine the value of k > 0 such that dx x (x? + k?)² %3D 32 1

A: ∫1x(x2+k2)dx=∫1x3+k2xdx=∫(-xk2(x2+k2)+1k2x) dx=1k2ln(x) -∫xk2(x2+k2)dx=1k2ln(x) -∫x(x2+k2)k2dxLet…

Q: 4. What is the value of k ?( Let P(t) = 246.7 and P(0)= 226.5 at t =10) А. 0.00243 В. 0.000854 С.…

A: As bartleby expert we are required to solve only one question.  Answer : k= 0.00854 Hence option C…

Q: Consider the following conditions. x = 73.26 O = 8.25 n = 38 %3D Test the hypotheses H: H = 79 H: u…

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Q: 1. Prove with the usual notations that: (a) EV = VE = A (b) A +V =- (c) A= SE Apply the suitable…

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

Q: * 10% of f we seloct e flems sold during pr obabilitfese Sold by online 9s ea ne turned a day, find…

A: We want to find the following probability

Q: 12. If IN = 2x + 10 and AT = 26, find x. %3D %3D В 丰 N A O 6 O 12 О 10 8. -

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Q: Let S = {:n e N}. %3D a) Show that inf S exists b) Show that inf $ = 0

A: given S=1n:n∈ℕ to show  (a) infS exists (b) infS=0

Q: B// Evaluate the following integral: fx³ n* dx.

A: We integration by parts and logarithmic properties  eln(x)= x  ln(mn)= n ln(m)

Q: S 1.Prove that L (coswt): %| s2 +w2

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Q: that Edn H(n/d)7(d) = 1 and Edn H(n/d)o(d) = n for all n, where r(n) = d(n) and σ(n) = σι (n) Σm d.…

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Q: π/2 The integral f/2 fossin drde is equal to O-1/2 O 1/2 01 00 10

A: We have to find the integral ∫0π2∫cosθ1sinθ drdθ .

Q: 7. Find the value of cosh (In3) O a. 3 5 O b. 5 O c. 5 3 O d. 3

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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: Q: Prove that : sin' ne -de = na for all n e N. sin' e

A: solution is given below

Q: 10. Prove the following statement by contradiction. “V odd inte- gers a and b, 4 { (a² + b²)."

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Q: -108 AD = 12.363 ((-1.2278 × 101'T² + 6.1946 × 10°T + 6.015 × 10 UT 80 Use Use Simpson's 1/3 Rule to…

A: We will use Simpson rule to approximate integral

Q: Z1 is complementary to 2; 2 is complementary Given: 2 B 3 A E to 23 Prove: BD || AE

A: Prove that BD∥AE.

Q: Use Shapiro-Wilks and a = 0.05 for the test and show all parts. * %3D Но: (а) На: (b) F and PValue…

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Q: If f(x) = (15)× then f'(x) = ? %3D O a) In(15)* O b) In(15)(15)*

A: using differentiation formula

Q: 1I. Find. the.mte...changef.fat.P.in.tha.divection o.then.ectenc ūif: ..+ fr.yin.x... d... 2 3 .. ..

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Q: 5.) Which of the following illustrates 4D E F inscribed in O M?

A: To determine which  of the following illustrates ∠DEF  inscribed in ⊙M

Q: Q7: Prove the following: 1) Pr(A) = 1 – Pr(A) 2) Pr(S) = 1 3) Pr(A n B) + Pr(A n B) = Pr(A)

A: Since you have posted multiple sub-parts, we will solve the first three sub-parts for you. To get…

Q: Evaluate the following 17 dæ J 10x(In(x))5

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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: 10.) For n>Liestablish that the in teger nc an't 5) is of the form ok. or n21, establish the in nz1…

A: To establish given relation we will use first principle of mathematical induction. For this we will…

Q: Which condition would prove ADEF-AJKL? 7 21 D. A. DE JK = 1:3 O B. DFJL = 1:3 O C. EFKL = 3:1 D.…

A: Here we will find the correct condition,

Q: H.W. Re-Solue the above example oith 4 following FCS) = %3D Ses?+S+5)

A: Given function is, Fs=4ss2+s+5 Taking the roots of the denominator, s2+s+5=0s=-0.5+2.2i, -0.5-2.2i…

Q: (-1) is where n is an integer. equal to the above e(1+2n)i where n is an integer. equal to the abov…

A: We know from eular formula e^iθ = cos θ + isin θ

Q: in a paragraph proof please

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Q: Q5: Find the Z-trans form of the following: Hint: af(k) = F (=) a) x(k) = 2k ek b) x(k) = e-k sin wk

A: Z transform of 1 is: ∑k=0∞1.Z-k=∑k=0∞Z-k              =Z01-Z-1              =ZZ-1

Q: 2) Evaluate each of the following. Show your work. pIn(3) e2t +5 dt et a)

A: Given:        (a): ∫0ln(3)e2t+5etdt

Q: Result n! de!... dn! Sn has permutations of ky pe [1i2* nte]

A: