1. Show that b, = (n!)'/n > 20.

Q: A sequence sn is said to be bounded above if there is some number N such that %3D Sn SN.cO S,2N.dO

A: Bounded Above Sequence: A sequence an is said to be bounded above if there exists a real number M…

Q: Show that the series Ln=l 12+2z10n-5z"ª –3z+2;10n converges absolutely for |리 < 1.

A: The series ∑n=1∞an is absolutely convergent if the series ∑n=1∞an  Ratio test:  The series ∑n=1∞an…

Q: 9. 4 to have od 8 OY Sum of int. Zs m/4= Sum of ext. Zs m28= dona bail

A: Note that, the sum of the interior angles of any n-gon is given by: (n-2)×180° And, the sum of the…

Q: 1+e-* Show that dr diverges.

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Q: 7.S dt J VE+2- 5

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Q: 4. P1,500 payable semi-annually at 6% effective o bn qon

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Q: Find d if z = log2 y - 6 logs y. In In 64 dz dz dy y In 2 In 5 dy y In 2 In 5 O Option 3 O Option 2…

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Q: A continuous annuity to (20) and (30) pays RM10,000 per year while both are alive and RM5,000 per…

A: According to deMoivre's law, if a living being has ultimate age of ω, then the probability that x…

Q: * Show that the sequence (xn)n>1 in R, where In = 1- Vn' converges to 1.

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Q: 20. Show that if E-1a, converges, then 1 + sin(a,) Σ n=1 converges.

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Q: If n = 18, then the interval of the form (- t(n-1), alpha/2 , t(n-1), alpha/2), that contains 99% of…

A: From the given information, number of observations n = 18. Confidence level  Level of significance

Q: 3. Find an orthonormal pair one of whose members is proportional to (4, -3).

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Q: 1) Use Simpson's Rule with n=4 to calculate S x² dx.

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Q: a random varrable Y has a cumdative df fy if 04 >4 probability hat Y falls between 2land 3 find thd

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Q: Assume that after w months,butterfiles populace in 1000 is calculated as F(w)=12w+cos(16w)+n×100…

A: Minimum and maximum of a function depends upon all the variables present in the function.

Q: Suppose that we observe that X1, X2, . . . , Xn  are iid∼ U(0, 1). Show that X(1) converges in…

A: A sequence of random variables Xn is said to converge in probability, denoted as Xn→pX, if…

Q: b) Is the Soluticn increasing or P N decreasia a when between o and te canyjug capacity

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Q: 2. Show that X H→ In x is increasing on (0,0) and that In 1 = 0:

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Q: 3, Re call Eudlid's proof of In finitude * primes! Shouw that T Cx): = 1{ ps X: p-pinae }12 logz…

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Q: 1. El radio de convergencia de la serie de potencias es (n+1)!

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Q: 51. For which values of a does eax dx converge?

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Q: Find the domain at the Furetion Iこ1パー25 rate in intervul Notation x4

A: Given f(x)=x2-25x4we have to find the domain of the given function

Q: 4.102. Show that ch(a+1)/c and then use this result to show that the important probability integral…

A: Answer is in the image below.

Q: If In x + In(x – 2) = ln(7x), then x -

A: From the given problem:   lnx+lnx-2=ln7x   Now using the logarithmic property:   ln(a·b)=ln(a)+ln(b)

Q: Show that the series Ln=0(2-1 1 6) converges uniformly on (z: Iz| 2 2).

A: Consider the given equation,

Q: 2. Z=e Iny

A: Given that, z = ex ln y x = ln (u cos v) y = u sin v We have to fin dz/du and dz/dv. Then we get,…

Q: 3. Consider the test of Ho: of = 03 against H1: of < o3. Estimate the p-value for the following fo-…

A: Given: Hypothesis is H0:σ12=σ22     Vs     H1:σ12&lt;σ22f0=0.27n1=10n2=8

Q: The sequence a, = sin (A) is unbounded (C) converges to a number less than 1 (E) diverges to…

A: Limit of a sequence

Q: The sequence {(1 + 1)^² +1} 2n O O converges to e² is divergent ez converges to e 2 O converges to e

A: Sequence

Q: converges, then C„-)" " con COr n=0

A: We have to choose the correct answer from the given option according to the given series

Q: 2. Rainwater accumulates in the ditch as follows: 10 centimeters of water in the 1st second, 15…

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Q: suppose the quantity of a substance, Q, decreases by 6.5% in 10 hours 1. find a formula for the…

A: The decay model is represented by,

Q: d tanh¬' (In t) = dt 1(1 – (In t)²)

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Q: Find lower bound for f(n) = 5n².

A: To find the lower bound for f(n) = 5n2

Q: is solved by New e initial guess of iterations would

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Q: What is the power series representation of the derivative/integral (whichever you chose in problem…

A: (3).  The given function is: f(x)=lnx2-4

Q: 8= From Orelinay Differeulial eguaton of following by Eliminaking the y==x(aCos 2x + bSin2x)

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Q: Find Residues by using Lourent's Series f(²)=3/²2 at Z₂ = FL

A: Given f(z) = zz2 - 1

Q: 3. Prove that So 0 1 x + ex -dx = n=1 (−1)n−1(n − 1)! nn

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Q: -B/ls//E-x] in (6.14) is distributed as at =

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Q: in c nurmal disribution X= S and Z= -1.23 thờ tlis Yon that X-5 the mean Stardard devictens to The

A: It is given that X = 5 and z = -1.23.

Q: 18. Show that Ein d(k)³ = (Ekin d(k))² for all positive intege m

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Q: If xy In( 6 sinh( 6x)), then x2 y'= Select one: O In( 6 cosh(6x)) O None O 36 x coth( 6x) - 6 In( 6…

A: The given function is - xy = ln(6 sinh(6x))ORy = ln(6 sinh(6x))x We have to find x2y' where y' =…

Q: 4. Evaluate the following integral fel e(-²²-25) dt

A: Note:-  ∫ e-x2 dx=π2 erfx +C   Given integral is ∫0∞ e-t2-254t2 dt

Q: Determine the one dimensional DFT for the following sequence x(n)= { 0,\ / 7 / l }

A: Sol:- Given Sequence :- xn=0,1,7,1One Dimension DFT  is given by Xw=11111-j-1j1-11-11j-1-j0171

Q: S az lnz (In z + 1)dz z In

A: ∫azlnzlnz+1 dz Put, z lnz=u⇒1·lnz+1z·z=dudz⇒lnz+1=dudz⇒lnz+1 dz=du

Q: 5. Show that the sequence Pn = 1 converges linearly to p 0, and the sequence Pn = 10-2" converges…

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