1. Try to use the ratio test or the root test to determine if the following converge or diverge. If the test does not work, use another test: T n +2 3 (n2 +1)(n+ 1) (c) ) cos"

Q: Consider the following equation f(x) = a3 – 3x2 + 3x – 1 = 0, [0.5, 1.5] Determine a function g(x)…

A: given fx=x3-3x2+3x-1 with interval 0.5,1.5 a)  put x=0.5 into the equation of function…

Q: (d) Calculate the integral 1 dr, x (In a)P and thus show that it converges for p > 1. Carefully…

A: (d) given integral ∫2∞1xlnxpdx claim- to calculate the integral and show that it converges for…

Q: The approxinmation of the root x of the function f(x)-r-5x'+9x +3 in the interval 14.6 accurate to…

A: Secant's Method Of Iteration             xn=xn-2-f(xn-2)xn-1-xn-2f(xn-1)-f(xn-2)

Q: (4) The general solution to 7xy" – y + 10y = 0 is y = A x + x+ x²+ x3 + ... -) +В х x²+ x³ + + x+…

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Q: 6. Consider the integral f(n + 1) = x"e¯* dx where n20. CGive a convincing argument that S* x"e¯*…

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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: dx converges and, if so, to what. 49. Determine whether J = | E/1* I-

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Q: 7. Find the radius and interval of convergence. (л — 2)" a) > (x + 1)" b) n 3n+1 nº 5n n=1 n=1

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Q: if the Positive root aso: ax²+x-1=0 it is calculated using the recurring formula X₁+1 = 1 = a (x₁)²…

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Q: V2+cos (n2+1) Use the basic comparison test to determine whether E1 n=D1 converges or n+en diverges.

A: To check the Convergency of the given series. We apply here Simple comparison Test and Ratio Test of…

Q: Prove that the seugences or series of functions converges pointwise but not uniformly on [0,1] 1.…

A: We have to show that the following sequence or series of functions converges pointwise but not…

Q: Given that n21 and xn = V5n2 + 2n -3n 00 1. Will {xn}, be divergent or convergent? 2. Will E=1Xn be…

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Q: Consider the function f(x) = Inx+2- whose graph is given below. (a) On the graph, illustrate how…

A: Draw a tangent line at f(x0) and if it crosses or cuts the x-axis then that point is x1. The Newton…

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: b) Suppose (xn) does not converge to 0. Then there exists e > 0 such that all except for finitely…

A: Let us suppose the following sequence xn=1,0,1,0,1,0,..... We have to see that the odd terms are 1…

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: .Does 00 sin? (n) 2n n=1 converge or diverge? Use any method and give reasons for your answers.

A: Here for the series we use Dirichlet’s Test:

Q: Do the following scquences {a„} converge or diverge? Justify your answers. (a) an = 3 (b) an –…

A: "Since you have posted a question with multiple suparts, we will solve  three subparts (d), (e) and…

Q: Discuss the Convergence or Divergence for D { [4+ (-0"]" (Z+2)" こう 2n+1 - DZ² 2 لع Wi ngo (2n+¹)!

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Q: 1.2 Determine whether or not the series of functions {Sn(x)} = {>*-1} converges uniformly k=1 on…

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Q: 6+ cos (7x) Perform a test to determine if x converges. T/ 7 00 5 dx X II

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Q: The radius of convergence of Eo(3n + 1)! (x + 5)" is: infinity none of the other options

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

A: According to Bartleby's policy we are allowed to solve only 1 question at a time. Here's the…

Q: (2r + 3)" =1' V 2n +n – 1

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Q: For which z's does the infinite series 1+ 좋 + + +. zn + . 3" 27 converge? To what function does it…

A: The solution are next step

Q: cos(nT) n=D1 converges conditionally in Select one: O True O False

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Q: Q2: If the positive root of the equation f(x) = ax + x- 1 is calculated using the fixed point method…

A: Let's find.

Q: decide if the given statement is true or false,and give a brief justification for your answer.If…

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Q: Σ 4(k!) ² (2k)*! K=( a. Converges completely because re? b. diverges because r=? C. ratio test is…

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Q: 4) ( The function f(x)=x'-5x +3x+9 has a double root at x= 3. Use a) the standard Newton-Raphson, b)…

A: a)

Q: 1. Find the interval and radius of convergence 00 (4x – 2)" (-1)" (4n + 1) n=0

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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: If lim M→0 J1 rM dx converges, then which of the xP Following must be true? elect one: o a. Σ…

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Q: d 23 a Show that dx :(-{e-*(sin x + cos x) ) = e¬* sin x. N. 00 b Find e* sin x dx, and show that…

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Q: Q 12.11 whot values of does this Seirics seines converge? n (in u) n=2

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Q: 5). Find the interval of convergence. ∞ n = 0 xn n7 + 8

A: Introduction: A power series can either be convergent everywhere or can be convergent over a…

Q: 8+ cos (7x) Perform a test to determine if x converges. 3 n/7 9 dx x3 1/7 (Type an exact answer,…

A: Given integral :

Q: For which values of p does E=1 (1+eon)4p converge?

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Q: 1.3 write the fallowing integral (a) e | Determine whether the folawir Converges or diverges. x- 3x°…

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Q: 10.Does 00 sin? (n) 2n n=1 converge or diverge? Use any method and give reasons for your answers.

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Q: If |Xn+2 − Xn+1| < |¤n+1 − xn| for all n E N then (xn) converges. -

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Q: n! +5) A) diverges cos 40320 B) converges

A: We will apply Ratio test to check convergency

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

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Q: The interval of convergence of E=1 (x+3)" is n2 -4 < x < -2 the above None of the other options

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Q: (b) Use the Weierstrass M-test to show that E(cos.x)". 4 n=0 converges uniformly on [A/4, 37/4].

A: The series is given by: ∑n=0∞cos x2n,    x∈π4,3π4 Now, ∑a2n=a0+a2+a4+... Now, cos function lies…

Q: 1 i. Use the result in (i) to test for convergence 2n =1 2 Vn? +5

A: See the attachment

Q: 4) Consider the function given by (-1)*+' (x-7)* Ax) = E n =1 Find the interval of %3D convergence…

A: The function is  f(x)=∑n=1∞ (-1)n+1(x-7)nn

Q: 3n Problem 1. Determine whether E test(s) you use. z=1 n² -6 converges or diverges. Clearly state…

A: see 2nd step.

Q: The iteration Xn+1 = 2 – (1+c)xn + cx, will converge to a = 1 for some values of c (provided that xo…

A: Given Equation: xn+1=2-(1+c)xn+cxn3=f(xn) and this iteration converges to α=1 for some c To find c's…