1 1 COS COS | n² (n + 1)² 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: (In n)" c) E-1 2n+3 n! cos NT b) Σο n=1 n%3D1 n3+n+2

A: Consider the given series: Here the objective is to check whether the given series is convergent or…

Q: 7x Cos + COS cos 2.

A: According to trignometry formula:cos a +cos b =2cosa+b2 cosa-b2Given,cosx2+ cos7x2a=x2; b=7x2

Q: 3 Find the exact values of s in the interval [0,2x) that satisfy the given condition cos 2s = л 11т…

A: Topic : trigonometry

Q: (a) Show that z" + z=" = 2 cosn0. (b) Hence show that 32 cos5 0 = A cos 50 + B cos 30 + C cos 0…

A: Given:- Let z= cosθ+ i sinθ

Q: 4. Given 0 ≤ 0 < 2t, solve cos 20 - cos = 0. 0 0, 풍, 풍 0 0, 1, 2 ○ 쓩, 쓩 01.2

A: see below the answer and calculations

Q: 7) y=Flx)=cos" (x) A.) xCcoskl) =4 Cos? (x) %ax (coscx) =4 cas? (x) (-sin(x). 4 Cos (x)Sin(x) %3D…

A: Explanation of the answer is as follows

Q: 4. (an)nen with an = n sin- 2n sin(2n) 5. (an)nen Wwith an = Vn 6. (an)nen With an = Vn2 + n-n 7.…

A: See the attachment

Q: 2. an = 3 +- + cos(2nz) п 3. an = In(14n – n) – In(3n° + 2n² + 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: The number of solutions to cos 0 = – c, with 0 < c < 1 and O 2 Infinitely many

A: This question can be solved graphically.

Q: ( 5) Find f (o) and f (0) f Ga)= .3 if x° Cos (x3)

A: Taylor series expansion

Q: 10. Solve the equation over the interval [0,2n) cos (20) = 5cos (8) – 3

A: Given :- cos(2θ)=5cos(θ)-3 To find:- solution of equation

Q: The number of solutions to cos 0 = - e, with 0 <es1 and sos 2 Infinitely many

A:

Q: (-1)"n" sin" () Σ n 2n n=1

A:

Q: Cos 30° Sn 60° o S.n 60° Cos?0° (os 60° S.n šo° %3.

A: As per our guidelines we are supposed ro answer only 3 parts, those are given in the steps below.

Q: 1 1 1 cos a + cos 3a Cos a + cos 5a 1 Cos a + cos 7a +.... + cos a + cos(2n + 1)a 1 cosecaftan(n +…

A: Given that, We have to prove that, Consider the nth term of the left-hand side, By using the…

Q: e identity: cos 3x = 4 cos x-3 X So

A: # we are entitled to solve one question at a time please resubmit the other question if you wish to…

Q: 2|C|k°]Re{el°• = k°{A cos(bln k)+B sin(b ln k)} 3 In k + B sin 2 [(4)-}. /3 In k 2 k1/2 { A cos

A: Equation 8.87 is a property   By using this property we can solve the equation Here  r  is a complex…

Q: S(1) =-cos (21) + e² 4. e

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: 3. cos 20 de –2p cos 8+p2 , p| < 1 [). 2np2

A:

Q: The series 2 cos(n t) n = 0

A: By integral test we can solve the following problem

Q: 21. The general solution of 2 cos2 x – sin a -2 =0 is of the form x = An, b + 2nn, +2rn, n EI. The…

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Q: 3-26 · Evaluate the integral. 3. (x cos 5x dx

A:

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: 1. Find the particular solution to y' = 3sin(x) given the general solution is y = C - 3cos(x) and…

A: Topic - differential equations

Q: Σ (-1)" (2n + 1)! Given: sin x = ,2п+1 for x E R n=0 (-1)"(2n + 1) Compute the exact value of the…

A:

Q: |(9 cos(9 x) +4 sin(4 x))dx =sin(9 x) - os Select one: True O False

A:

Q: 1. In(6n) n4 - 2 3. n(In(n))2 %3D2 4. 1 5. nyn sin (4n) 6. n2 n=1 2.

A: We use different kind of series convergent set.

Q: 15. The values of 0 that satisfy the equation 2 cos20 + cos 0 -1 =0,0<0 < 27, are 5 3. and 6 2 6. 57…

A:

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: The sum of the series 1 + 2" + ... is n! ... 1! 3! A In 2 B e' cos 2 D sin 2 E nonexistent

A:

Q: 2) If z = cos 0 +isin 0 show that 1 = 2 cos 0 a) z+-D 1 b) z" + 2 cos no %3D

A:

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

A:

Q: 7. a) 3[cos (800) + iSin (800)] X  4[cos (700) + iSin (700)] b)   10[cos (3500) + iSin (3500)] /   5…

A:

Q: (-9)" (2n)! n=0 (a)e³ (b) cos 3 (c) co (d) sin 3 (e) None

A: The given series is ∑n=0∞(-9)n(2n)!

Q: 7/20 2 cos X 1 dx = ? X 22n+2 22n (a) E(-1)"- (b) E(-1)". (2n).(2n)! (2n + 2).(2n + 2)! n=1 n=1…

A:

Q: 0.3- Prove that: n 2n 1 (cos =0 +i sin8) + 10 2cosne - 5 eine

A:

Q: 1 cos Cos (n + 1)² n n=1

A: A telescoping series is any series where nearly every term cancels with a preceeding or following…

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…

A:

Q: 3 Find all solutions of cos 2x for x if 0 < x < 2n. 2

A: The solution is :

Q: -11m. ii. cos-1(cos()) CO 6.

A: Given problem:- cos-1(cos(11π6))=?

Q: (2n + 1)п' 4 sin =? (2n + 1) n=0

A: The given series is: ∑n=0∞sin(2n+1)π4(2n+1)

Q: 40. Show that cos(30) = 4 cos e - 3 cos e for all 0. [Hint: cos(30) = cos(20 + 0).]

A:

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

A:

Q: 12. Find all values of 0 in the interval [0, 2n) that satisfy the equation: cos 20 + cos 0 = 0

A: We need to find value of θ.

Q: A s(1) = e-7" sin(8 1) () = e" sin(3 1) © s(1) = e3 sin(7 1) Os() = e-5 cos(71) D

A: