E1 (arctan(2n+1) – arctan(2n – 1)) n=1

Q: sin(7n) A 1. n2 (-7)" C 2. n=1 (-1)" A 3. 4n + 5 (n + 1)(2² – 1)" - 4. 22n Vn 5. (-1)", n+ 5 C n=1

A: 1. the given series is ∑n=1∞sin7nn2 the given series converges absolutely. therefore, the correct…

Q: Part 1: 1 1. S *(In x)3 dx 2. Se3x cos x dx 3. S(1 + x²)e-*dx 4. So x²e*dx

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Q: meª (In x)-5 Find: What is the behaviour of y as →→ ∞ ? Given: Y- ▬▬▬ Oy -∞ Oy →∞ Onone of the above…

A: Please see the below picture for detailed solution.

Q: cos x – 1 dx = ? 22n 22n+2 (a) E(-1)". (b) Σ-, (2n).(2n)! (2n +2).(2n+2)! n=1 n=1 22n+1 22n-1 (c)…

A: Given, I=∫02cosx-1xdx I=∫02cosxx-∫021xdx now solve both integral…

Q: Question 12 If the solution to e2x sec2(e2x+1)dx is equal to ktan (e2x+') + C, find the exact val S…

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Q: 1 1) [ (tan³ 0 + tan³ 0) e-tan º d0== 2 (-1)" n! (In x)" dx= (m + 1)"+1 ·

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Solve the given DE x?dy - xydx-2ydx

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Q: 28. The general solution of the equation tan(2x +) = It A.2x = nn - -B. 2x = nt +"C. 2x = nT + D. 2x…

A: According to the guideline we should have been able to solve only first question of the demanded…

Q: sin x – x dx = ? X 22n (a) E(-1)". 22n+2 (b) E(-1)". (2n).(2n)! (2n +2).(2n+2)! n=1 n=1 22n+1 22n-1…

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Q: 1 Find the L-1 s(s²+2s+5) Oetsec 2t e-tcsc 2t 으글e-tsin 2t et cos 2t

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Q: メ- 148 %3D E = 0-91 %3D Level of Con fidence

A: Given : Sample mean (X¯) = 148 Margin of Error (E) = 0.91 Level of confidence = 95%

Q: 263 X dy a. Solve the differen tial equa tion 7s 263 sin x) cošar) +xe"

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Q: iox e dx solue with Residue nethod 2 - x + 2ix +1

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Q: n #1. E(-1)" n = 1 Vn° +2 n cos nT #2. n = 1 2" # 3. E(-1)"(/n+1- /n) n = 1

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Q: Approximate the sum of the series correct to 4 decimal places

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Q: 2 sin x - x dx = ? 22n (a) (-1". 22n+2 (b) E(-1)" - (2n).(2n)! (2n + 2).(2n +2)! n=1 n=1 22n+1 8.…

A: Consider the given information: To find the integral ∫02sinx-xxdx. Here option (c) is correct.

Q: 32 e こと dz と+e Use gamma or beta laws with the solution in detail of

A: The value of the given improper integral is π/8

Q: COS X -1 dx = ? X 22n (a) E(-1)" (b) E(-1)" 22n+2 (2n +2).(2n+ 2)! (2n).(2n)! n=1 n=1 22n+1 (c)…

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Q: 9n – 5 a) lim n-- 3-n - 18 1 2n2 + 3n – 5 8n? +1 1 b) lim n- o0 || 4

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Q: 4. -π/4 1 9cos² x-sin²x dx

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Q: 2. xp- X2 a. b. + C с. + C d. None of the above dx 3. x(1+x) In xin (1+x")+C b. xarctan (1+x')+C a.…

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

Q: Q3) Express cos(x²) as a power series. а) 1. 2! + 6! 4! x10 + 3! x14 +. 7! b) 1– 5! c) 1– x5 x7 + 7!…

A: To express the function cos(x2) as a power series. Here, note that the power series of the function…

Q: (-1)"zən+1 (2n + 1)! sin = 3! (-1)"-2" (2n)! 21 1+r+ (-1)*+1," I+1) -E n-1 2! Pip- 1)(p – 2)a.. 3!

A: f(x)=f(0)+xf'(0)1!+x2f''(0)2!+x3f'''(0)3!+x4f'''(0)4!+ ⋯ +

Q: 15a) n=0 (-1)² 7³² (2n)!9" 2n+1 15b) (−1)" 3+¹ 00 n=0n!5"- 15c) √ x³ sin(x²)dx

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Q: 1.4 = 0.9062 x Cos (1-√³x) dx = 0-6034 How?

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Q: e) S„ =E(-1)". sin (5 +n5) Vn+1 e) S. = n=0

A: Note:-  Sum of convergent and divergent series is divergent. cos2x=1-2sin2x⇒sin2x==121-cos2xput…

Q: cos √x+1 O Σ n=2 (-1)"x²" (2n)! n+1 x² Σ nal

A: I have given the answer in the next step. Hope you understand that

Q: || cos( 30-1 )d0:3 cos( 30-1 )d0>=S2.cos cos (30 -1) de

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Q: 33. If z = [i(cos 0 + isin 0)]" then arg(2) -2n0 + n A n0 + n 2n0 D 2n0 – n

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Q: 00 2n+4" (1) E n=1n+6"+1 (2) En ( 3) Σ cos [(2n+1)!]? (1-2n)" 00 00 1 (4) E n" (5) E arctan n n=1

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Q: sin x - dx 3 ? 22n (a) (-)". 22n+2 (2n).(2n)! (b) E(-1)" (2n +2).(2n + 2)! n=1 n=l 22n+1 8. 22n-1…

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Q: 2. 3. ત્ર 6 -1 cos²2x dx X - dx

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Q: . Dctcrinino the constant k such that the cqua- tion (x2 + 3xy) dx + (kx² + 4y) dy = 0 is exact, and…

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Q: cos(b) = >. Σ (-1)" b2m for all b e R (2m)! m=0 Given the integral of cos² x dx, express it as…

A: Given that,Cosb=∑m=0+∞-1m2m!b2m for all b∈ℝTo find: ∫01cos2xdx  in terms of a series of constant…

Q: sin x – x dx = ? %3D 22n (a) E(-1)". 22n+2 (2n + 2).(2n+ 2)! (2n).(2n)! (b) E(-1)"- n=1 n=1 22n+1…

A: ∫02sin x-xxdx

Q: (-1)" (2n+1)! n=0 Σ Given: sin x x² n2n+1 for x E R (-1)"(2n +1) 4" (2n + 1)! Compute the exact…

A: Given: sinx=∑n=0∞-1n2n+1!x2n+1 for x∈ℝTo compute: The sum ∑n=0∞-1n2n+14n2n+1!

Q: 10. Evaluate: e-y ** [In(x + y) - dy dx A. α2 a² [In(2a) – 1⁄In(a) − ³] + Ei(-a) − In(a) – In 2 + 3…

A: To find- Evaluate:  ∫1a∫0xlnx + y - e-yx dy dx

Q: Find y''of 4cos(x/2)+e^-2x

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Q: 2 sin x – x dx = ? 22n (a) E(-1)". 22n+2 (2n).(2n)! (b) E(-1)"- n=1 (2n +2).(2n+2)! n=1 22n+1 (2n…

A: If the integrand has a convergent power series representation, then it can be integrated,…

Q: (a) (arctan(n + 1) – arctan(n + 2)) n=0 ω Σ 1 In ( 1+ n=1 1-n (c) > n2n n=1 (d) E(-1)"n²e¯" n=1 cos…

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Q: Solve the given initial-value problem. The DE is of the form- dy = f(Ax + By + C), which is given in…

A: The solution is given as

Q: 3n 2n n S " S"(sin x + cos y)e? dx dy dz 2n 'n A. 2n(e2n + e3™) в. 2п(е2т — езт) c. 2n(e3™ + e2") D.…

A: Given: I=∫2π3π∫π2π∫0πsinx+cosyezdxdydz   We know that; ∫sinxdx=-cosx+C∫cosxdx=sinx+C∫exdx=ex+C And…

Q: 2 sin x – x dx = ? 22n (a) E(-1)"- 22n+2 (b) E(-1)". (2n).(2n)! (2n+2).(2n+2)! n=1 n=1 22n+1…

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Q: TL 12+3i-2 (e) lim 71 00 n3

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Q: 1n 1-Co1 2n

A: To evaluate ∫π4π2 sin 2x1 - cos 2x dx

Q: 1 - T <x< T Ans. 4 cos(x) +cos(2.x) - 4 1 ***+ (xɛ)soɔ- 4) f(x) = 12

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Q: 4 E(-1)" sin n=1

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Q: 2. Prove the reduction formula: (5 pts) n-1 sin x cos n - n-2 | cos" xdx = cos" xdx

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Q: Enei Jan-19snk[(2n – 1)8] = %3D Select one: CO a. súnh(sink8) 4 Obsink(sink8) 4 3. o d. sinh(4sink8)

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