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: Let 2a4 + y* + 23 = 4 Then dz (1, 1) = 8/3 -8/3 none of the listed here 1

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Q: 2. Show that In (- - ) = ( + 2nn)i where n = | .... .... ..

A: Consider the following expression: x=ln-12-32iex=-12-32icosx+isinx=-12-32i

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Q: + 2x Compute dæ. O 3(z+z²) +C 1 1. I미 피 + C 2 O x +2 ln |æ|+C

A: Given: I=∫1+2xx2dx

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Q: 7. Show that Sx" Inx dx =Inx-+ c. n+1 %3D + C. n+1 n+1]

A: Using integration by parts we can prove the given integral.

Q: 00 dt

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Q: 35. Prove: If xn = :o(an), then xn = = O(an). Show that the converse is not true.

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Q: 6. Find f'(1) if Ax) = nx

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Q: 23n 23. 5h+1 n=1 а. О b. 1 c. 2/5 d. 8/5 e. Divergent

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Q: Then Suppose f(x) dx = 13 and 8 12 4 [ 12 13 and ["fl f(x) dx = f(x) dx = 5.

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Q: Show that e = o (hª) as h → 0 for all values of q.

A: Like big O notation, there is also a little o notation. There is a difference between big O and…

Q: 4. Show that inf {1+ ¼n: n EN} = 1 %3D

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Q: If a > 0 and [[ 20*+v 20+u° dr dy = 1(e* – 1) , a =?

A: Using polar coordinate evaluate the above integral

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Q: (2 2" (2"-1)a - 3 If A = then A" = Éro* +1) = -m(n + 1)(a° +n+2) 4 5 Ertr-1)=,n(n² - 1(3n + 2) 12…

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Q: b) Let S = (/n .ne N}Uu(1+3/2n •n € N}u {6 – /3n•n € N}. Find S' and sups.

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Q: 22) let XnN20, 036), iF P(X<W) = 0.05 th the value of wis

A: Given that, X~N(μ=20, σ=0.36) To find the value of W when P(X&lt;W)=0.05

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Q: Q₂: Evaluate 8 dx 6 x + 1

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Q: For the case n = 10 and m = 20, interpret the result for E(X) (write one sentence in English to…

A: Here given equation  of expected number of bins remain empty