Suppose x1 : 1/2 and xn+1 := xn2. Show that {xn} converges and find lim xn.

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: 2. Determine if S dx is convergent or divergent. x²-x

A: In this question we have to determine if this integral convergent or divergent. If limits exists…

Q: Calculate whether it is convergent or divergent. (4x)2* x=1

A: Given series is ∑x=1∞(4x)2xexx2x

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

A:

Q: Use series to evaluate the limits

A:

Q: - Find the interval of convergent for : 2n 2 2n! n=0

A:

Q: Find 2x dx. x2-4 (if it converges)

A:

Q: 16 dx

A:

Q: Suppose x1 : 1/2 and xn+1 := x(n/2). Show that {xn} converges and find lim xn.

A:

Q: Examine the convergence of ,where a>1. (log x)" +1

A: First I have told about Improper integral of first kind and then using it evaluate the given…

Q: Given that lim n²(x– 5)" converges by the Ratio test. If x € Z then the numerical n- 00 value of x…

A: This is a problem of power series.

Q: {VI2n + 8 – V12n} converges or diverges. If it converges, find the limit.

A:

Q: +o0 (-1)*n" sin" () Σ 2n n=1

A:

Q: 1 -dx xln*x 1.

A: To determine if the following is a convergent or divergent. ∫e∞1xln4xdx Solution: A indefinite…

Q: 1 n4 + sin“ n=1

A: To find that the given deries diverges or converges

Q: (2n+1)! (x-2) n=0

A: We have to find the radius and interval of convergence.

Q: Suppose to solve for a root of f(x), i.e., ƒ(x*) = 0, we use the iteration Xk+1 = ¢(xk) where o(x)…

A:

Q: 2) is E=1 2n convergent?

A:

Q: If lim a, is not 0 then 2 a, is convergent n=1

A: By using theorem we can say that

Q: Given that lim n2(x-5)" converges by the Ratio test. If xEZ then the numerical 1- 00 value of x is…

A:

Q: find the Limit of each convergenl 2n t 1 An = 1 - 3Vn

A:

Q: 9. Determine by the root test if Ln=2 (4n-5\n 2n+1, converges or diverges.

A: Explained below

Q: Prove that sina de converges but not absolutely for 0 < p < 1. XP

A:

Q: Determine if  ∫3-2(1/x^3)dx  is convergent or divergent.

A:

Q: 59. Show that 1- sin x dx converges. x? 00

A:

Q: Does sin () x 7 converge or diverge? Why?

A:

Q: Q1-) Determine whether the following functions are convergent or divergent: 1 1- En=1 ((3n-1)*/…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If xi 2, 3dn-1+ 3"n-2 show that {xn} is convergent. identify the limit.

A:

Q: Use series to evaluate the limit. 4 3 sin(2x) – 2x + lim 4/3

A: Given problem:-

Q: Find the radius and interval of convergence for (-1)"(x – 1)" n4" n=1

A:

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

A: As the mention in above given question when x goes towards infinte than function f(x) gives 0. It…

Q: B. Find out if E bn where bn = n* sin" -Converges or, 2en -Diverges (Show complete solution using…

A:

Q: The function ƒ(x)=x' – 2x - 4 has a root at x = 2, write one re-arrangement of the form x1 = g(x„)…

A: The given function is,f(x)=x3-2x-4

Q: find if diverges or converges. if converges, then find its limit cos²(8n) An 8n-1

A: Given - an = cos28n8n - 1 To find - find if diverges or converges. If converges, then find its…

Q: Vn +1- n –1 n=1

A:

Q: The radius of convergence (2n + 3)! (x- 1)" is | None of these infinity

A: Given ∑n=0∞(2n+3)! (x-1)n Compare it with ∑n=0∞ an(x-x0)n Then an = (2n+3)!an+1 = (2(n+1)+3)! =…

Q: . Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (²) < 0, ƒ (x) has a root in [0]. To…

A:

Q: 10. (x- 3)" Ln=1 n

A:

Q: Use series to evaluate the limits

A:

Q: If 2 Cnx" is convergent when x=2 and divergent when x=-3, then 2 Cn is n=0 n =0 convergent. O…

A: Consider the given information: The series ∑n=0∞Cnxn is convergent when x=2 and divergent when x=-3.…

Q: Find the exact value that the sequence sin" 1 converges to. (Note n=0 that as usual, sin" x means…

A:

Q: n sin"(n) :) has a convergent subsequence. Vn2+2n Show that (an) = (-

A: Consider the sequence an=nsinnnn2+2n We have to show that sequence an has a convergent subsequence.…

Q: If a fixed point iteration for solving F(x) = 0 is given by g(x) = x+ c(x - 5) with xo = 2.5, what…

A: The fixed point iteration formula x=g(x) converges for x=x0 if g'x0&lt;1.

Q: Given that {an}n=1_is convergent such that a1 = V5 and an+1 V5 an- %3D Solve for lim an n 00

A:

Q: Use series to evaluate the limit. V1+x-1 1 ーX lim

A:

Q: Find the interval of convergence for the function (x-5)" g(x) = > Σ 3" Vn + 2 Make sure to check the…

A:

Q: Use series to evaluate the limit. X-In(1 +x) lim

A: Find your answer below

Q: 1 ·dx (х + 1)2 -2

A:

Q: Find the interval of convergence of Ln=1 (r-1)" 2n

A:

Q: find if diverges or converges. if converges, then find its limit cos² (8n) an where n 2 0 8n-1

A: