Indicate which of the following are correct, and correct the ones that are not. (a) In e* = x (b) e³el/3 = e (d) In 2+ In 4 = In 8 (c) In 3 = In 2

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Q: and g(n) is O(H), the

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Q: Show that inf n e N} = 0. n1/3

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Q: If (ar + br) = 2n %3! n+1 and k-1 8. E(ak - br) = n+2 - , then ar %3D k-1 k-1

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Q: e20 do 10. 1+ 3e20

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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: Find E (X) and E(X²) and using these values evaluate E[(2X + 1)²]

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Q: 3. Given n > 1, let S = E-1: Show that S, is not k=1 _k° an integer.

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Q: 3 E in (1 -) -in2 , . =-In2 =1 k2 –1 k=2

A: We will  use the limit of partial sum

Q: 2. Evaluate the following dr 2.1.V1-(In)* dr 2.2. VE(1+ z) dr e-e- 2.3.

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: a) Show that E-o(-1)*(")=0, and then verify that () + C) + C') + -- - C) + (") + (") + -- .. b)…

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Q: 1000 1000 2. Find Eb, if E(4b, – 5)=16. k=1 k=1 1000 1000 1000 1000 1000 а. —1290. b. Уь, —1254. с.…

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Q: Show that E-o (-1)*(")=0, and then verify that () + C) + C)+ - = (") +C) + () +-- -G) + G) + G)-…

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Q: What can you say about z if |e|= 1. Ques

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Q: nx) in the E 2n is

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Q: 6. Show that =+ E-(-1)"(n+ 1) E)". when Iz – 2| < 2.

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Q: Write In (e5 x 2) in term of In x. In (e x²) =

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Q: 9 /Find A and A by Hamilt on Hheorem for A= E125 -75 -IS

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Q: FOR N=195, by fermat's theorem an-2 =

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Q: Let I be ar. V. has a Binomial dist. B(n,@) with the Pid.f. fex; G)o-0^,X:o,n Show that fex;)…

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Q: Which method can be used to prove AEFG AG H. LL E.

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Q: (15 49)} = at* e²¹ sen(71), et 2-¹ {-98 (8-2)² +49)} = What's the value of a*c?

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Q: O None of these Oe equal to the above Vdows O is equal to the above O is equal to the above 434

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Q: Calculate E(X³), where X has the following PMF: .5 x=1 f(x)=.3 x=2 2 x=3

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Q: Evaluate the following. In(eº) %3D =

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Q: If var(e) → 0 as n → 0, then 8 is said to be

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Q: -In 3 e* In 2 V4 - e*

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Q: show that for positive epsilon, |x-4| |3x-12|<e

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Q: find the general for al soluh'an 3yC3) (e)

A: The given differential equation, y(4)+3y(3)+3y(2)+y'=0