Which of the followings are divergent series? 542" 1. E 00 2+2 00 1 n-1 4n2-1 μ1. Σ ( sin 1 )" 00 n3D1 IV. cos(na)"/2 O a. I, II Ob.I, IV Od. IlI, IV O e. II, II

Q: For how many of the following series we can use the nth – Term Test for divergence to obtain the…

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Q: Examples. For each of the following power series, identify the centre a and nth coefficient cn. ( 0)…

A: To find the center a pf the power series and nth coeffiecient.

Q: (b) Obtain 3 non zero terms of the Maclaurins series for sin²x. Hence, evaluate sin² x 0.5 1.0.5 5…

A: The given problem is to evaluate the given definite integral using Maclaurin series of sin2x upto 3…

Q: Which of the following series is a convergent Geometric series? 6" a) OE 5" n=1 bb Σ1.05)" n=1 5 c)…

A: To find the Convergence of geometric series.

Q: e cos(2)d.z 4. Evaluate as a power series. Write out the first three nonzero terms

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Q: Q. 29. Calculate harmonic from the following continuous series: Class Interval : 0-10 10-20 20-30…

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Q: (-1)" d) Find the sum of the series En=0 n! using the Alternating Series Theorem correct to three…

A: To find the sum of the series we must know about the series of ex , putting x=-1 in the series of ex…

Q: 1. Does the following series converge or not ? cos(n) CO Σ n=1

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Q: 1 se a power series to approximate the definite integral dx to 6 decimal places. 1+x4 hter the first…

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

Q: Find the trung of the followir series given tl

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Q: which of the following series are not convergent? Select one: a. Lk-0 , sin(kt) O b. Ek-0 55t1 O c.…

A: As per the question, we need to find one series which is not convergent. Let us start from option…

Q: (-1)*x2* 1. For all x E R, cos x = (2n)! n=0 b. Differentiate the series in item 1(a) to find a…

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Q: The value of ao for cosine series on interval [0,]for ƒ(x) = x is Select one: a. b. 0 C. d. NOT e. 1

A: The Fourier cosine series of a function f(x) over an interval [a,b] is given by;

Q: Which of the following infinite series converge? * cos (tan-n) i) En=1" -n=1 ) En=2nln(n) 1 (n +1)3…

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Q: Determine whether the given series is convergent or divergent. 5" + sin? n a. Σ 3" - | sin n| 7 b. E…

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Q: The following telescoping series sin converges to tan '(0,5) converges to tan *(0.5) O This option…

A: Option D is correct..

Q: 7. By using power series representations, find the function corresponding to given series n+2 E(-1)*…

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Q: 5. Integrate the following using Maclaurin series. Leave your answer as an infinite series. e* dx а.…

A: (5) (a) Given the integral is ∫exxdx. Integrate the integral using Maclaurin series.

Q: (b) Obtain 3 non zero terms of the Maclaurins series for sin? r. Hence, evaluate 0.5 sin² x dx. Give…

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Q: By replacing cos(z") with the partial Maclaurin series you found in part (b), compute the exact…

A: Solve the following

Q: For what value(s) of p does the series below converge? 10 cos(+2) n² n=1 Select the correct answer…

A: Sol:- To solve this Problem , let us consider first p > 0 (So take any value , Let p = 1)…

Q: Which of the followings are divergent series? 5+2" 1. 00 II. En=1 4n-1 I. E (sin1) IV. E cos…

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Q: a. Ln=1 n+n cos?n 3. Using any method, determine whether the following series is convergent or…

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Q: 1: Find the arclength of the a, curve V1 - x, 0 < x s 1, Is the given series 2 - 1 + 2 1 + 4 ... a…

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first one. If you…

Q: Which of these series, if either, converges absolutely kTT sin 1.E(-7)* I.E k-1 k/k k-1 A. I only B.…

A: To find whether the series are absolutely convergent

Q: Which of the following is a power series about x 0? O Vx + v2x + V3x + v4x +... O 1 2 3. 4 +... x2…

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Q: Approximate sin (x²) dx with the first 3 terms of the MacLaurin series for sin (x² ). 1352 1155 14…

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Q: For how many of the following series we can use the n'h - Term Test for divergence to obtain the…

A: The nth term test for divergence is : If  limn→∞a_n≠0 then the series converges If limn→∞a_n=0 ,…

Q: Evaluate the following indefinite integral as an infinite series: Sre* dx. Hint: We will get a power…

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Q: The Maclaurin series for cos x is Eo (-1)"; What is the n%3D= (2n)! coefficient of the term forx*?…

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Q: Q: Apply Taylor's expansion and The series for tann at 4

A: Taylor Series expansion of f(x) about the point x=a f(x)=∑k=0∞fk(a)k!(x-a)k…

Q: ect the divergent series A) SEL B) 7 sin n10 tan C) D) arctan 9" tan n10 5+1 E) F) 9" In 1+ 5+1 5+1

A: By different methods of series for convergence and divergence, we can identify the nature of the…

Q: - Develop the Maclaurin series for cos (2x) eep to terms in X4 what is the greatest truncation error…

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Q: Which improper integral would you use to help determine the convergence/divergence of the series Ln…

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Q: Problemm 2: Find a series that converges to the valve of the integral. s' ? orctoncsa?) dax. Show S…

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Q: Which of the following series is convergent? (1) to cos(nn) 5n+1 (1) E (II) E n? !5+2n² (III) E +00…

A: 1)  ∑n=1∞ cos(nπ)5n+1 cos(nπ) = (-1)n ∑n=1∞ (-1)25n+1 Here limn→∞ 15n+1 = 0   and 15n+1 is…

Q: 45. $[.. cos (n) how many terms are needed to give an approximation accurate 1 3n²-5 Given the…

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Q: Which of the following infinite series converge? 3n(n²+2) (n +2)³ 1 n(Ln n)? tan-(cos³(n²) ) 5n°+7n…

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Q: Which of the followings are convergent series? I. 5+2" Ln=1_2®i2 II. 0 Ln=1 _4n²-1 II. (sin1)" n=1…

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Q: 2. (a) Find the Maclaurin series representation of f(x) = x cos State the radius of convergence, R.…

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Q: which interyal of convegence 2birect of -S) tPower series Ž Lx - (8) (e) -00 (0) co,lo)

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Q: Which of the followings are convergent series? 5+2" 1. En=1 2+2 II. E-1 1 Ln=1 4n?-1 00 1. Σ1sin1) "…

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Q: x?e* Use power series to evaluate lim X- 0 cos x -1

A: To evaluate the limit of the given function by using power series expansion.

Q: Compute the value of the following improper integral, if it converges. (If it diverges, enter oo if…

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Q: 20 Use a power series to represent the function f(x) centered at a = 0. = 15x4 +4 Provide your…

A: We have to find the power series of f(x)=-2015x4+4 centered at x=0. The power series expansion of…

Q: select the divergent series SELECT A) B) 6" In 1+ 5+1 6th D) S6" tan| 5+1 5+1 n-1 E) F) arctan sin…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Q(5) the second term of Maclaurin series generated by f (x) e-* is: (a) x (b) -x? (c) -

A: I know the Maclaurin series for e^x and by replacing x by -x we get the solution

Q: 3 + cos 5k 27. E k3 k=1

A: Given series, ∑k=1∞3+cos5kk3 The objective is to determine whether the series is converges or not.

Q: Which of the following series converge? . Σ3n7 II. En=2 n(In n)? 1 cos(nn) III. E=1 %3D1 2n-3 A) II…

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