Show that a Possion RP X(t) with rate lamda is mean-square continuous even though no sample path is continuous. The definition of the MS continuity is lim E{(X(t+e) – X (t))²} = 0. for t> 0

Q: The improper integral A) S = f(z)dz has an infinite limit as k s to infinity goes I f(z)dz B) S = |…

A: A integral is said to be convergence if integration of function over the interval is finite I.e…

Q: Let x1 > 1 and  xn+1 = 2 − 1 / xn for n ≥ 2.  Show that ( xn ) converges and find its limit.

A: Given - x1>1 and xn+1=2-1xn for n≥2 To prove - xn is convergent and also find its limit .

Q: If limy- f(x) = 0, then f(x)dx converges Select one: O True O False

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Q: Show the uniformly converge to F Fn CX) = X 12 Fn (X)= X 1X€ (-10] XER %3D

A: We know that if a sequence of function has bounded derivative the uniformly convergent

Q: Show that the following method is convergent, and determine it's global order of accuracy. 1 At (Yn…

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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: Show that if Σ i=1 converges towards a € R , then lim ) a; = 0 i=N

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Q: Find the radius of convergence for: (- 1)"x" Vn + 7 TL=1

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Q: Find the lower bound for the radius of convergence for (x2 + 6x+ 10)y′′+ (x2 −4)y′+ x2y= 0 about x0…

A: Since given point x0 is an ordinary point of the given equation obtain the singular points and thr…

Q: A manufacturing company owns a major piece of equip -ment that depreciates at the (continuous) rate…

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Q: By using the substitution t² determine the convergence of = S ∞ dx (x+1)√√x*

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Q: 1/x e 7 dx y3 -1

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Q: Suppose lim y(t) = 5, which initial value problem does y satis dy A. = 25y – y", y(0) = 6. dy В. =…

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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: If f is a continuous function on [0, ∞0) and | f(x)dx converges, then I f(x)dx diverges. 3 Select…

A: Given that, f is a continuous function on [0,∞). And, ∫3∞f(x)dx  converges. Then,…

Q: How to prove that the function h(y)= sum_{m+1} ^infinity (m+y)/(m^2+y^2) converges to a continuous…

A: We are given a series given as, hy=∑m+1αm+ym2+y2 We need to show that the above series is…

Q: 00 6n–1 Зп+2 1 Apply the nth term divergence test to conclude if E converges or diverges.

A: The divergence of a series can be found using the nth term test. Consider the series . Let . If…

Q: Use the Limit Comparison Test to determin 8" + 1 n = 1 9n + 1 g"+1 lim =L> 0 n-- O converges

A: Given series is ∑n=1∞ 8n+19n+1 find whether the series is convergent or divergent

Q: If the function f is continuous on [0,00) and | f(x)dx is convergent, then there is a possibility…

A: If the function fIs continuous on [0, ∞) and ∫1∞f(x)dx is covergent, then there  is a possiblility…

Q: Show that for the function f(x) = x'x the steepest gradient descent converges after one iteration…

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Q: Find an upper bound for the Lagrange interpolation error for f(x) sinh(x)+2 cosh(x) over the…

A: Given: fx=sinhx+2coshx, x∈0,2. Interpolation nodes xk=k4, k=0,1,⋯,8. To find:          An upper…

Q: Compute the point-wise limit of (fn) and determine if they converge uniformly on given intervals. 1.…

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Q: a growing population of rabbits on Br'er Island can initially be modelled by the CApe 13 model, with…

A: Given that: N=N0et/2N=BC+e−t To find the value of B and C in terms of N0 and Nc.

Q: Show that the following method is convergent, and determine it's global order of accuracy. 1 At Yn+1…

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Q: Give an example of a sequence of continuous functions: fn: [0, 1] R that is pointwise convergent but…

A: Consider the function fx=0, x is irrational in 0,1mn, x is rational in 0,1. This function is called…

Q: 2 Q/if the function fc)=ĕ is not Continuous at T where =TIL x<T foint the fourier Scries of fcxeě is…

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Q: Let fn(x) x + n a. Show that fn(x) converges pointwise [0, 0). on

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Q: 2+cosx 1. Use the comparison Theorem to determine whether dx is convergent or divergent

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Q: obtain a slope field, and add to it graphs of thesolution curves passing through the given points.…

A: Given: y'=2y-4; 0,5 for finding solution of given equation, we use variable separable method so,…

Q: Let x1 O and xn+1 x+1 2 Show that (x,n) converges and find its limit.

A: It is given that  x1=0 and xn+1=xn2+12. Let xn+1=ϕ(xn)=xn2+12 By fixed point iteration method…

Q: Classify the critical point (0, 0) as to type, and determine whether it is stable, asymptotically…

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Q: If lim=c>0, then both convergent and both divergent. ylgn O Ihi O

A: If limn→∞anbn=c&gt;0, then ∑bn,  ∑an both convergent and both divergent. (a) True (b) false

Q: 1 -dx x In*(ex) 1. e

A: Topic = Integration If the limit exists and is a finite number, we say the improper integral…

Q: Find an example of a sequence of continuous functions {fn} defined on the interval [0, 1] such that…

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Q: 2. Let 3nr? + cos nr In (r): %3D (a) Find the pointwise limit of (gn) on R. (b) Is the convergence…

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Q: What is the role of the curvature condition, , in ensuring convergence of a line search algorithm? O…

A: The role of curvature condition in convergence if a line search algorithm is concluded as follows:…

Q: Construct a sequence of continuous functions fn : R →→ R such that 0 < fn S 1, limn-o Jo fndx = 0…

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Q: Suppose that = p(y) is an autonomous equation satisfying all four of the following dt conditions:…

A: Given that dydt=p(y) that satisfies the given condition.  i.e. py=y+3y-52      dydt=y+3y-52…

Q: Suppose f and g are continuous functions. Provide an example such that | g(x)dr diverges 0. adf(x)dr…

A: Follow next step

Q: b) Use the Comparison Theorem with f(x) = - to show whether , g(x)dx is convergent or divergent.

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Q: Let f : [0, 1] → R be a continuous function. Show that the sequence of functions 1 fn (x) = ,x +1 +…

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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: obtain a slope field, and add to it graphs of thesolution curves passing through the given points.…

A: We have to find the slope field and add to it graphs of the solution curves passing through the…

Q: Let y = 5x² + 4x + 4. If Ax = 0.3 at x = 4, use linear approximation to estimate Ay Ay ~ Submit…

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Q: Classify the critical point (0, 0) as to type, and determine whether it is stable, asymptotically…

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