13.D. Show that, if we define fn on R by fa (x) 1+ n?x? then (fn) converges on R.

Q: 1.2 Prove that if {fn(x)} is a sequence of continuous functions on I which converges uniformly to…

A: We have to show that f is continuous on I.

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Q: 4. (5pt) If f(r) = [t – 1) cosh t dt, on what interval is ƒ increasing? (Hint: Use the Fundamental…

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Q: Σ 1 sin kæ) is uniformly convergent on (-0, 00). Show that k2 k=1

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Q: 1) Does cos" cn) Sin*™(n) converges uniturmly on D, : [0, K14] ?. And on

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Q: Theorem 64. Let {pk}1 converge to point If y # x, then {pk}1 does not converge to y. x.

A: Given that sequence pkk=1∞ converges to point x.

Q: 18 For which numbers a does x,+, = a{x,– x) converge to x* = (a – 1)/a?

A:

Q: 1 (a) Use the Integral Test to show that > converges. 2. n' +1 d 1 n = 0 -1 tan dx Hint: 1+x?

A: As per our guidelines, we are supposed to solve only one question.  Kindly post other questions  as…

Q: 8. Let f : R → R be uniformly continuous on R and if fn(x) = f(x + ) for x E R, show that (fn)…

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Q: (x + n)² Show that h„(x) converges poimtwise to f(x) = 1, V x e [1, 00). %3| x² + n²

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Q: Suppose fn : S → ℝ are functions that converge uniformly to f : S → ℝ. Suppose A ⊂ S.  Show that…

A: Suppose fn : S → ℝ are functions that converge uniformly to f : S → ℝ. Suppose A ⊂ S.  Show that the…

Q: 1.₂0 +00 1 2. Determine whether the integral da converges or rvin x diverges. If it converges,…

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Q: 3.3 Prove that does not converge uniformly on R. k! k=0

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Q: The approximation of the root x of the function f(x) = 2x +5-e in the interval [3.4] accurate to…

A: Thanks for the question :)And your upvote will be really appreciable ;) Need 3 iteration

Q: Question 9 For n21 and r E R, let fn (x) = 1+n?r?° (a) Show that (fn) converges on R. (b) Is the…

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Q: 1² + 11 For what value(s) of n, the integral dr converges? Justify In + 8x2 + 2 your answer.

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Q: 5. Use the comparison test to determine if each integral converges or diverges b) 2 2/3-4 a) e-x² dx

A: Solution: 5.a ∫1∞e-x2dx

Q: 4.1 Suppose that fig and g'are continuous on the interval 1= {x :asxs b). Show that a ) exists, and…

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Q: 3. Show that the improper integral x*e*dx is convergent and gives the answer of 4! (It turns out…

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Q: (x-1) The following improper integral ; (x+1)(x²-x+1) converges to 2ln (4)

A: Improper integral.

Q: (b) Prove that the improper integral ]] 8888 converges. dr dy (1 + x² + y2)3/2

A: Solution: Given improper integral, ∫-∞∞∫-∞∞dxdy1+x2+y232 As we know the convergence of the series is…

Q: Suppose that 0< fn < In on X for all n e N. If gn 30 on X, then fn 30 on X.

A: Solution:-

Q: 1. Evaluate the following Improper Integral. Does the limit converge? Why or why not? [Apply the…

A: According to our guidelines we can only provide solution of one problem at a time, therefore i have…

Q: 16) If E an converges, then cos(am) diverges. n=1 n=1 a) True b) False

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Q: which true? Converges point wise to fi[o,1]→R where flx) =2 forallxE [u] "() ( 2 Pn)n is increasing…

A: It is given that fnx=exp(-xn)+1 for all x∈0, 1 and for all n∈ℕ. Check the pointwise convergence and…

Q: 19. Suppose f and g are positive-valued continuous functions such that f(x)s g(x) for all x25. If…

A: given,

Q: 3 If Xn 4 and ly,l0. Select one: True O False

A: Given, xn → 4  and  yn≤31n2n for all values of n To determine whether ∑ xnynp  is absolutely…

Q: 4. Consider the sequence of functions {fn}=2 where fn: [a, b] R defined for n > 2 by if 0 < x <- fn…

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Q: Consider the sequence of functions n+ cos(x) 3n + sin(x) defined on the R. 1. Find the function f to…

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Q: +9 for all n2 1. Prove that {r,} converges and find 2.1 4. (a) Let r = 4 and am+1 its limit.

A: Sometimes, a sequence is defined recursively. In that case, to test the convergence of the sequence,…

Q: Σ Suppose that ax" converges to a function y such that y" – 2y' + y = 0 where y(0) = 0 and y'(0) =…

A:

Q: 1. For r < 1, define fn(x) = ²x. (a) Prove that for x < 1, k=1 ƒ(x) = lim_ƒn(x) = 84x x(1+x) (1-x)³…

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Q: k+ln k > ak, where aj = and ak+1 ak k+10 %3D k=1

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Q: The sequence {G 3n+2 n=1 O None converges to e O diverges converges to Ve? converges to e3

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Q: If fn If 0 ≤ an ≤ bn for all n € N, and f on [a, b], then lim ſå fn ‡ få f. an converges, then bn…

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Q: 9. Let a be a positive value. State the integral test, and use this to determine whether ). -an e…

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Q: 2.62 Show that fn(x) = x+n converges uniformly on [0,1] but not on (0, 0).

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Q: 9. Let a be a positive value. State the integral test, and use this to determine whether > -an e n=0…

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Q: 5) Find all values of x for which En=1 nxn (n+1)(2x+1)n converges absolutely.

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Q: Determine the values of p for which f(x)da converges where f(x) = = 1-e-z TP

A: Here, in the question for what value of p the integral is convergent. The simple improper integral…

Q: O Discuss the convergence of f,(x)=x + , on A =[0,00).

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Q: If |fn(x)| < an for all x and Ln=1 an converges, prove tha En-1 fn(x) converges uniformly. n=1

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Q: 2.68 Suppose fn(x) = 1-". Decide whether or not f, converges uniformly on each interval, and prove…

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Q: 1.- In the following problem, find the Riemann sum for the given function on the indicated interval.…

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Q: Suppose that fn(x) and f(x) are functions R –→ R. Suppose also that fn converges uniformly to f as n…

A: Suppose that fnx and fx are functions from ℝ to ℝ such that fn converges uniformly to f as n→∞.  To…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.