2 72 Given n is a positive integer, (V3 + j)" + (V3 - j)" is 2n+1 sin O () 2" cos 2" sin (") 2n+1 cos

Q: ſcos 3t sin 8t dt * 1/2 (-1/5 cos5t - 1/11 cos11t ) + C O 1/2 (1/5 cos5t - 1/11 cos11t) + C O None…

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Q: 3.4 Find the residue of f(2) = (1 – 2º) sin(1/2).

A: Find the residue of f(z)=(1-z^6)sin(1/z) We know that residue of f(z) is the coefficient of (1/z) in…

Q: (-1)" (2n+1)! Given: sin x = En=0 x2n+1 for x e R 100 What is the exact value of the sum 2n=0…

A: The series given is: sin x=∑n=0∞(-1)nx2n+1(2n+1)!, x∈ℝ...(1) To find the exact value of the series…

Q: The integral of the given function | cos(9x) cos(5x)dx is equal .. 14 sin 4x + 4 sin 14x А. · + C 12…

A: This question can be solved by applying the formula of 2.cosA.cosB

Q: Choose the most appropriate answer: Evaluate the integral : (e- 18z + sin 11æ) dæ -18z cos11 +C 18…

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Q: n the der natwe of Sin (x )= Sin Cx-cos (rE)) to CoS

A: Definition: Differentiation is the action of computing a derivative. The derivative of a function y…

Q: (-1)" Σ Given: sin = x²n+1 for x E R (2n + 1)! n=0 (-1)"(2n + 1) 4" (2n + 1)! Compute the exact…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

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: +√√² cas² S 4 cos²20 de is One of the correct steps to evaluate @ 1²00-1/²160²20 4 de- A sin²20d0 Ⓒ…

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Q: Given: sinx = (-1)" (2п+1)! x2п+1for x € R n=0 Compute the exact value of the sum 0-1)"(2n+1) „2n+…

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Q: 1. Eliminate the Arbitrary Constant(s) of the following: 1. by xy'-1; b is constant, 2 y=+de; e and…

A: We have to eliminate the constant in the given equation. Here I am solving first two parts…

Q: "ind no E N such that for all n > no sin(n + n² cos(n²)) n3 – 5n4 – 20 -

A: Find n0

Q: Evaluate the definite integral: 7/4 1+5 cos2 (t) dt cos? (t)

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Q: 1 1. n=1 /n 00 2. E ne ne n? n=1 3. n(In(n))2 sin (7n) 4. n2 n=1 5. Vn n1- 2 6. 3.

A: Note: " since you posted multiple question. As per our guidelines we are supposed to solve one at a…

Q: 3.4 Find the residue of f(2) = (1 – 26) sin(1/2).

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Q: Use the properties of logarithms to write the expressions in Exercises 43 and 44 as a single term.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 1 (27 x sin nxdx 27 bE f(x)sin nxdx -sin nx -1. 1-2n cos 2nn COs nx %3D %3D The requirod f 2)

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Q: 3. Which of the following is the particular solution to the ODE. y" + 4y = cos(2x) 1 x sin(2x) 4 A.…

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Q: 32. If 2 sin 0 cos 0 cos 0 =0, where 0 <0 < 2n, then the exact values of 0 are 57 0, 3 O0, 5. 7, ,…

A: Given : 2sinθcosθ - cosθ = 0 Where, 0 ≤ θ ≤ 2π To find : Exact value of θ?

Q: 7. Let z1 = 3-j; z2 = -2 +j8, find cosh {sin [In (1 + z1′ + z2")(√ − z1″ + z2')}" 8. Refer your…

A: 7.Hint: Here the values of z1 and z2 are given. Differentiate the values as required and calculate…

Q: 1₂ O 2² x² + x2° In | co - 3 2 O O None of the choices O +∞ dx In 2

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Q: 3. Verify that u = e cos x is a solution of + 8² = 0

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

A: Sum of the series, using Taylor series expansion

Q: Let z = 3 -i and w = -2 – 2v3i . Evaluate . O a. V3 3n (3n +isin ) cos w Ob. V3 +isin () cos V3 (cos…

A: we will use following identities to evaluate given expression  a+jb = a2+b2 ∠ tan-1ba and A∠θ1B∠θ2 =…

Q: (1) List the first 5 terms of oach of the soquence (a,). n+1 (d) an = sin An = 3n- - 1 3(-1)" (e) a…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Prove that Σ n=1 sin ne n - 6.² < sin x X - dx = 1.8519... for any positive integer m and any 0 in…

A: In this question we have to Prove the following given statement. ∑n=1m sin nθn&lt;∫0π…

Q: Which of the following is true for the BVP y" + 16y = 0, y(0) = 1, y () - = 5 with Yg = c1 cos(4x) +…

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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…

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Q: Let m be the number of solutions of sin (2x) + cos (2x) + cos x + 1 = 0 in 0<x< x< 1/1/2 and 7 7π n…

A: The roots of the equation: f(x)=0 are the values of x, where the graph of the function: y=f(x)…

Q: 7s+15 Find L-1 s+2 O 7 cos (v3t) + sin(v3t) O 7 cos (v2t) + sin (v2t) O 7 cos (v2t) + sin(v2t) O 15…

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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: Given x[n] = x1[n] + x2[n] where, Ttn x1 [n] = 9 cos and x2[n] = 8 sin 4 8

A: Given: xn=x1n+x2n x1n=9cosnπ4 x2n=8sinnπ8 To do: Graph x1n using Scilab.

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: 15n + 12n sin n? n² n-3 n=2 W?

A: Part (c) Given series is

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

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Q: 7.32. Prove that for 0 sxSr, - ( (* .) cos 2r 12 (a) x(w-) cos 4x 22 cos 6z 32 6. (b) æ(r - 2) = 8 /…

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Q: (-1)" p2n+1 (2n+1)! Given: sin x for x E R n=0 (-1)"(2n + 1) 4" (2n + 1)! Compute the exact value of…

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Q: 3.4 Find the residue of f(2) = (1– :4) sin(1/2).

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Q: ſcos15x cos4x dx * 1/2 (1/11 sin11x +1/19 sin19x )+ C O 1/2 (1/11 sin11x) + 1/19 sin19x + C None of…

A: Solution

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: 8. Let 2ni S7 = e7 = cos- 27 + isin- 7 7 a. Prove that E¢ = 0 k=0

A: we have ζ7=e2πi7=cos2π7+isin2π7we have to prove…

Q: 5 + 2 sin(n?) n=1 n2 (b) Σ Vn5 + 100n² +1 n=1 In n (c) E(-1)*+1; n4 n=1

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Q: 21 +2.T.0 () +2-т-0 3 • k = 0: V512 ( cos 2 (cos (-) (–)) = 2 cos () – 2i sin () + i sin 3 COS 9. +…

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Q: Solve for O on Co, 2T) 6 sinio + 9 cos 0 -9-0 2 Sin O + 3cos o -3=0 Sin O +los? = Sm?O =1- cos?O…

A: Form the given trigonometric equation in the quadratic equation than solve by factorisation.

Q: 5 a) Write down the form of particular Colutiun to こ for each of the following g (x) g (n) 4 CoS6x -…

A: The solution for the required part is given as

Q: Can i get help step by step?

A: Given integral is WE will use following substitution to evaluate the integral

Q: St² sin(2t*)dt A 1 (sin(2t*) – 2t*cos (2t*)) + C (sin(2t*) – 2t*cos (2t*)) + C 14 B D (sin(2t*) –…

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Q: 35. In the integral x €, 1), which values of x satisfy the -3n 2 equation cos x 2 а. 1 b. 2 с. 3 36.…

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Q: #2: Which of the following statements are always true? (i) The only solution to cos x- for x in [x,…

A: Given query is to find the correct statement.