Define the sequence of functions {Jn(x)} on [0, 1] by 2n?x; 2n(1 — пх); 0; 2n fn(x) = 2n くE Find f(x) = lim fn(x)

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: In the function:  f(x)= (3x^2)ln(x) , x>0 What are the vertical asymptotes?

A: Given function is,

Q: a) limn-o fn(x) for each r E [0, 1], and b) lim,- So fn(x) dx.

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Q: The sequence V(n + 5)(n + 7) – n} is A) Convergent to 0. B) Divergent. C) limn-»0 V (n + 5)(n + 7) –…

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Q: 00 Fn+1 { is convergent, and Show that the sequence Fn n=1 1 Fn+1 lim n→∞ Fn Fn+1 > 1 and Fn-1…

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Q: If the sequence of functions {f} converges in measure to two functions f(x) and g(x), then these…

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Q: The sequence an =n-Vn +1vn+3 converges to the limit A)-3 B) -1 C) 1 D) +2 E) -2 F) 0

A: Given:

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

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Q: (d) Let x* = 1/2(2*), and what is the limit of x* as k 0? What is the order of converge for x?

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: lim 4 sin(x + n) + 3

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Q: for r20. Exercise 5. Consider the sequence (fn)n defined by fn(x) D 1. Find f(x) = lim,+o fn(x).…

A: We have to solve given problem:

Q: Express the limit as a definite integral. lim 40 E xk A xk; [-5, 1] k=1 1 9x8 dx -5 x9 dx x9 dx x dx

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Q: Find Limit of .... as n approaches infinity    an= ((-1)^n)/n^2 bn = e^n /5^(2n)) cn = ln(n)/n^5

A: Definition used -           limn→∞(a)n=0a<1∞a>1           We can use the L'hospital rule when…

Q: > If f is a continuous, decreasing function over [1,0) and the lim f (x)=0, X00 then :)dx is…

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Q: Let            fn(x) = nx/1 + nx2  (a) Find the pointwise limit of (fn) for all x ∈ (0,∞).

A: Given : fn(x)=nx1+nx2; To find the point wise limit of this function for given values of x: We have…

Q: If a converges to a(z) then lim / a (2)dz= / a(z)dz n- 00 Y

A: True

Q: find the limit as x approaches infinity of (1+2/x)^x

A: Find the limit as x to infinity,

Q: 2) If x3 s f(x) sx for x in [-1,1), find lim f(x) if it exists. x-0 A) 0 B) Does not exist C) -1 D)…

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Q: [In (x+1) Evaluate the limit of the function f(x) =er as x approaches 0 using Table of Values…

A: Consider the function  f(x)=ln(x+1)x To find the limit of the function as x approaches 0 using table…

Q: 32. Find the limit of the series: x (1+x) (+x) 1+x2 A) B) xx X+x C) (1+x D) (1+x) E) x

A: Given series is,

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

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Q: 1 d.x x In (ex)

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Q: Express the limit as an integral (or multiple of an integral) and evaluate.

A: limN→∞3N∑k=0N-110+3kN

Q: 11. Suppose f and g are continuous positive functions. Provide an example such that diverges and…

A: We need to provide example for convergence.

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: (a) Evaluate the following limit: lim ) (1-e3x x²+3x, x-0 (b) Find the equation of the tangent to…

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Q: (b) Let X and explain whether the sequence X = (Xn) converges or diverges. (xn) be defined by xn =…

A: We have to solve 4.b

Q: Find the value of ſ (2x – x³) dx by evaluating it as the limit of sums.

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Q: Q2/ Find the final value of the sequence {xk} with Z transform 4z2-z F(z) %3D 2z2-3z+1

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Q: n 5. Consider the sequence of functions {fn (x)}n given by fn(x) for XE [0,1] and 0 otherwise. Show…

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Q: Let ƒ(x) = (3x - 1)/x. Make tables of values of ƒ at values of x that approach c = 0 from above and…

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Q: We define an arithmetic sequence of functions: fn: [1,0) → R recursively as: fi(x) = Vx, Vx € [1, 0)…

A: Given fn:[1,∞)→ℝ recursively as: f1x=xfn+1x=x+fnx for all x∈[1,∞). (a). Let x∈[1,∞), therefore:…

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

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

Q: Let x1 = 1 and define xk+1 = sqrt(2xk) where k is a natural number. Prove that the sequence {xk} for…

A: Given: x1=1, xk+1=2xk So, x2=2x1=2>x1 x3=2x2=22>x2 On generalizing, we get…

Q: 6ln (1+x) lim х>0 2е3х—2secx

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Q: Find the limit analytically: 2-4x lim 40 5+3x x? - 2.x -15 lim x 5 2. 3. Find dy/dx of:

A: A number M is said to be the limit of a function f(x) at x=a if for any arbitrarily chosen positive…

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: IV. Determine if the given is convergent or divergent. 1. dx (x2 + 1)² 1

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

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Q: Let fn → f, where if 0 <x < L3 (3 – x) if 1 < x<1 { fn (x) п-3 if 0 < x < 1 - and f(x) if x = 0 Then…

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Q: {fn(x)} = {n²x(1 – x)"} for æ € R and n = 1, 2, 3.... | 1.find pointwise Limit

A: The given function is, fn(x)=n2x(1-x)n

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: 4. Let (#1, y1) = (0,0) and let (n+1, Yn+1} = (2+ yn, 3 – Tn) for n > 1. Prove that (Cn, Yn) is a…

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Q: The sequence a=n-vn+1Vn+3 converges to the limit A) -3 B) -1 C) 1 D) +2 E) -2 F) 0

A: For a series ; if it converges then . If  the limit ; then the series diverges.

Q: find the limit as x goes to infinity of ln(x+1/x+2)

A: Evaluate the limit

Q: Give an example of a sequence of continuous functions: fn : [0, 1] → R that has no pointwise…

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Q: i) The area of the surface obtained by the rotating the curve y=V 36-x², -3<x<3 about the x- axis is…

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Q: Define the sequence of functions {fn(x)} on [0, 1] by { 2n2x; 2n(1 — пх); т. fn(x) : 0; n Find f(x)…

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Q: Find the limit of the sequence a, n! 1 1 e e Divergent

A: Answer and explanation is given below..

Q: ar converges if and only if lim a, = 0. r->0 ア=1 True False

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.