Show that 100 1 arctan(100) – arctan(2) + 1 Σ 1+ k2 k=2 < arctan(100) - arctan(2) + 1+ 22 1+ 1002

Q: Example 7-27. Let X1, X2, ..., X, be jointly normal with E (X;) = 0 and E(X?) = 1 for all i and Cov…

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Q: X sec10 can 1. Let u = 7 In х2 - 1

A: Given: ∫x sec107ln2x2 - 13tan7ln2x2 - 13dxx2 - 1.

Q: = 3. Find the pointwise limit g of the sequence {n} on I = [0, 0), where gn(x) = the E-definition…

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Q: 10. Show that the interval (0, 1) is covered by the open intervals In (1/n, 1- 1/n), n 2 3, but (0,…

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Q: 1. Using (2n +1)Pn= Pn+1-P-1: prove that P(x) = (2n-1) Pn-1(x) + (2n-5) Pn-2+(2n-9) Pn-3+.... - and…

A: Given : 2n+1Pn=Pn+1'-Pn-1' To Prove : (a) Pn'x=2n-1Pn-1x+2n-5Pn-2+2n-9Pn-3+ . . . . . .…

Q: 1 Let Sn + 1 iii) 1 +...+ n+1 n+v2n+v3 n+vn Find the lim sn by comparing the relationship among S,,…

A: Given: Sn=1n+1+1n+2+1n+3+....+1n+n To determine: limn→∞ Sn  by comparing the relationship among Sn,…

Q: Let bn : n° +n+6 for all n ɛ N. Find limn→∞ bn- 5n3+4

A: Given that bn=n3+n+65n3+4 and we are required to calculate limn→∞bn. Therefore, we are supposed to…

Q: Prove that the sequence xn has a convergent subsequence. 3n4 sin n – 4n cos n2 + 2 a) Xn 5n4 – 8n –…

A: We have to prove that xn has a convergent subsequence in each of the given cases.

Q: Prove that 1 1 1 Lim Jan+1 + V2n²+n. /2n²+1 V2n²+2

A: Limit is defined as the value of the function , when number of terms tends to infinity.  It can be…

Q: 1 Expand in ascending powers of x, up to and including the term in x', simplifying the V(1 –2x)…

A: To solve the following problem

Q: with Zeros of 2i with integer coeRficients that haf E Puno

A: We need to find the polynomial of degree three with integer coefficient

Q: (3k + 8)! Consider the series> ar k3k k-1 k-1 a) What is ak+1? ak+1 = aktl ? b) What is ak ak-1/ak =…

A: The given series,     ∑k=1∞ak=∑k=1∞3k+8!k3k

Q: 1. Find the Wronskian for yi = x , y2 = x² and y3 = x³.

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Q: Use Heaviside Expansion Theorem (2s^2+1)/[(s-2)(s^2-2s+5)^2]

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Q: How does Abel's Identity allow us to conclude that if the Wronskian is 0 at a point t, then the…

A: To prove: By Abel's identity conclude that if Wronskian is 0 at a point t, then the Wronskian is…

Q: 2. Let {an} be a decreasing sequence of positive numbers with limit 0. I define a new sequence…

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Q: 19. Find an interval of length i in [0, 1] containing a root of x - 5x +1 = 0.

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Q: 1:if z 1 then z is even " is false, we need to find z such that

A: Given statement is

Q: Example Suppose that Y Poisson(X) and consider testing Ho: A = A ild against H₁ A Av. solve it now

A: Given: Y~Poiλ

Q: Let 3 2 1. Verify that I4 = A. Show all of your work. 2. Verify that Alz = A. Show all of your work.

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Q: Determine the limit of the sequences (2 * n + 1)2 – (n – 1)2 an = (n + 1)2 – (n – 1)2 cos(42 * n3)…

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Q: Coefficient of ' in the expansion of (1+x) (1+ x)* is

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Q: all odd degree terms in the expansion of (x + v(x³-1)5+ (x – v(x³-1)5, (x > 1) is

A: Introduction :

Q: Theorem 9.4.3: The Prime Number Theorem. Let T(x) be the number of prime numbers in the range from 2…

A: Let π(x) be the prime-counting function that gives the number of primes less than or equal to x, for…

Q: Example 6: State the third congruence that is needed to prove AOZN = AELD by the indicated method. W…

A: Given,

Q: two positive iontages and bare by 2, them prove that. (2° +1) is most divisible by (2²-1) let a with

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Q: T-F If gcd(3a, 3b) = 6 then a and b must be relatively prime..

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Q: 18.lim(3z + 2) = 3i + 2 of the following statement is not true? zi A O(3z + 2) – (3i + 2)| < E…

A: Option (B) true because

Q: 1. Iff: [0, 1] R is defined as f(x) = x if x is rational, 1-x if x is irrational, discuss the…

A: Given :  f: [0, 1] →ℝ  is defined as     f(x) = x,if x is rational1-x,if x is irrational To find :…

Q: 1 find func- 88. Finding a Composition If T(x) = %3D Vi + Vx tions f. g, andh such that fo goh = T.

A: Given: T(x)=11+x To find f, g, and h such that f∘g∘h=T

Q: (2) Let f(x) = cos (2x). Find the Hermite interpolation H3(x) using xo = 0 and x1 = , and use error…

A: Given: fx=14cos2x We have to find the Hermite interpolation H3x using x0=0,x1=π4…

Q: 3 5 The Wronskian of {X2,x2}

A: The given set is: x32,x52

Q: 5) Prove that d tanh ) |-x2

A: Prove that  d/dx[tanh-1x] =1/(1-x2)

Q: Let the sequence {fn(x)} be defined on [0, 1] by n – n2x; if x E (0, ) fn(x) : otherwise SHOW THAT:…

A: The given sequence is fnx=n-n2xif x∈0,1n0otherwise First to find the limit function of this sequence…

Q: {Xn} 3. Prove that the sequence 1+2n² 1-3n² Xn where is bounded.

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: 2.65 Let fn(x) = xe¬nx² a) Find || fn||sup for all n. b) Determine whether or not fn converges…

A: The given function is fn(x)=xe-nx2 ∀x∈ℝ To find: (a) ∥fn(x)∥Sup ∀n             (b) Whether…

Q: (Xn) be a sequence of real numbers defined recursively by 1 = 1 and 1 7. Let X = In+1 =5(Tn +3) for…

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Q: the convergence or diver 3k Ek=1 k! 4k Zk=1 k2 - k

A: As per guidelines we have to solve only one

Q: The kth harmonic number is defined to be Hk = 1 + 1 2 + 1 3 + · · · + 1 k . Prove that for all n ∈ N…

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Q: Let yII + yI - 42y = 0 Find all values of k such that y = ekx

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Q: If (an) has limit−1 and (bn) tends to infinity, does it follow that only finitely many terms of (an…

A: No it doesn't follow the statement

Q: Choose {X}1 from [0, 1]. Let pn be the probability that X + X4+1 <1 for all i e {1,2,...,n – 1}.…

A: Given that Xi for i = {1,2,3,...,n} are distributed uniformly from [0,1]. Let us consider two random…

Q: 1) Prove that 2" 4 2) Prove that 4 divides 7" -3" for eachn E N 3) Prove that | sin na| 3 f(n) =…

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Q: 1. Find the first-order derives:

A: Given,      4x2+715x4+534x3-37x6+15x-30

Q: 2. Formulate the Three Sequences (Sandwich) Theorem. Calculate the limits of the sequences 5n +…

A: Sandwich Theorem: If {an},{bn} &amp; {cn} are three real-valued sequences satisfying an≤bn≤cn for…

Q: Let A={(-1)" Find sup A and inf A. Provide some explanations how you got their values or why they…

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Q: Let 0 < 0 < 1 be a rational number. Show that the sequence {cos(nT0)}-1 is divergent.

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.