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.

Q: 2 += cos 3t 3 -- sin 3t 4 3. L 20s? – 103s + 423 6. 28(s – 5)(s? – 9) 20s? – 103s – 423 20s2 + 103s…

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Q: 5- for y = (x² + 1)5 dx a)10(x² + 1)5 b) 10x(x² + 1)* c) (x² + 1)* 6- Sin 2x is equal to: a) sin x…

A: Answer of the above questions are

Q: S =m sin(3x)cos(5x)sin(7x) dx: (sin(5x)sin(9x) +sin(x)- 15 sin(15x) +C (लड 4 Select one: True False

A: Let's find.

Q: 2) Find L{te"sin5t} using two methods. ans: (s+2)2+25

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Q: Can i get help step by step with this problem?

A: Recall the following facts.

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.…

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Q: S tan5 x dx O 1/4 sec^2 x(sec^2 x - 1) - In Icosx |+ C 1/4 (sec^4 x - sec^2 x -In Icosx |)+ C O 1/4…

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Q: in Let z = 0.5 +",., Find e 6z 3 C) e3 F) e-0.5 (cos 2 + isin2) A) -e 20 B) e-5* (cos 20 + isin20)…

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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: 4. {sin(n)} 00 5. { In n=2 3 - n 6. 1- 3n J. n=1

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Q: 2 Z = 31 + (Sin 28 + ((ase Ÿ -(Sin@) Fined Iz1 12

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Q: 2a + acoth 2z ) dz \sin 3z a/2

A: We are given the integral: ∫a22a1sin 3z+a coth 2zdz Let I=∫a22a1sin 3z+a coth 2zdz I =∫a22a1sin 3z+a…

Q: 1 1. Find L{te"} ans: (s – 4)* 5 2. Find L{e# sin St} ans: (s +2)'+25

A: To find the solutions

Q: Complete the table below 1. y= sin x 3n 5n 7n 5n 4n 3n 5n | 7n| 117 2n 2n 6 7 37 4 4 3 3. 4 V3 1/2…

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Q: -24-4s e S COS os(28) – 7 sen(28) cos s+6 s2 + 49

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Q: 10. Find at x = 1, if e*y+1 = 3 dx A. In 3 B. In 3 – 1 С. 1 — In 3 D. In 3 1 E. e³ In(3) F. None of…

A: We have to find

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: What is L s+2 (s – 3)* - 9 e cosh3t +e sinh 3t 3. A. 3r 8. e sin 3t 3. B. e cos 3t + 3/ 3r 2r C. e…

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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: Answer: The approximate value of sin 29° is O sin 29° s 1( 29x 2 180 6)+ O sin 29° V3 ( 29x O sin…

A: Please see the explanation below

Q: 1²–1 True or False: cosh (sinh (In æ)) = Select one: O True O False

A: Given: cosh(sinh(lnx))=x2-12x. The objective is to verify the left hand side expression.

Q: Evaluate the integrals

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

Q: 4s – 20 s2 – 4 Select one: None of these O 4 cos 2t – 10 sin 2t O -3e2' + 7e-21 O 4 cos 2t + 10 sin…

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Q: Evaluate L{3(sin² 2t )} 24 24 24s 24 а) s(s² + 4) b) d) s(s² + 16) s(s² + 16) s(s² – 16) a O Option…

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Q: Therefore, 1 -3TS e 1 s +1 -3TS e -s +1 + 82 + 1 Y(s) = (s² + 1)(s² + 2s +3) s2 + 2s + 3 (s + 1)? +…

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Q: 3 L' ess [(s + 2)4 + 13(s + 2)2 + 36] 3e-24 u(t – 5) sin (2r–10) – sin(3t=15) ) sin(3t-15) 2. 3…

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Q: 2 +3 Evaluate S4) (-2) (22+4)(- dx. Enter In(x) for In(x), abs(x) for |x|, and arctan(x) for…

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Q: Find L{(1- t) (3 + 2 sin 5t)}. 3 10 10 O 3 82 s? (s² -25) 33 s(s² –25) 3. 3 10 10 - - 83 8(s2+25) s?…

A: L { (1-t) (3+2sin5t)} = L(3 - 3t +2sin5t -2tsin5t)   L (k ) = k/s L ( t) = 1/s2 L(sin at) = a/ (…

Q: 11. Find L{tU(t - 1)} A. В. е ers C. D. e-s 1 E. None --

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Q: 42. What is tan 0-1 Ove IN/MS/N/N 2 0_V2 2 O √3 377 4 2 ?

A: tan (π - x) = - tan x

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: L= {4 sin (3t) + 2 cos (9t)} L = {sin (2t) cos (2t)} 4s 6 2 + s2+1 s2 –9 s2+4 4s 6 + 82+1 2 s2+9…

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Q: () 13. У 3к = 4", Vn E N k k=0 14. L 2k = 2"-1, where n is even k=0 15. У 4* = 5", Vn E N k k=0 SIN

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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

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Q: • 8 If In = 7/2 e*cos" x dx, where n 2 2, prove that: %3D (a) In = 1-n[" /2 e-* sin x. cos"-1 x dx…

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Q: D n In (1+ n=1 n16 arctan E 5" In (1+ > sin n=1 2n+1 n=1 F

A: We have to choose the convergent series according to the given options

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: 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: Suppose m and n are constants and m + n. Evaluate [sin (mx) cos(nx) dx- A) Ⓒ[-(-)-(+)₁]+€ m+ncos (m…

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Q: 19/20 2 sin x - x dx = ? X 22n (a) (-1)". 22n+2 (2n+2).(2n + 2)! (2n).(2n)! (b) E(-1)". n=1 n=1…

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Q: Find L{(t – 1) (2 – 5 sin 3t)} . 2 2 15 15 + 83 s2 (s2 +9) 8(s2 +9) 2 15 30s s2+9 (s²+9)? 15 15 2 s3…

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Q: L (e*** sin 4t). 4e 4e s +16 (s+3) +16 O A.) B.) 4e 4e (s - 3)' +16 (s - 3)(s +16) O C) O D.)

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Q: 5. Evaluabe the following integraris s 471 sin thdz 24 C 1Z-i= 2 ans2 3. Co sh2 dz ,c: 1Z1=1 zsiz…

A: Complex integral

Q: '12 24 x sin' dx = 144 + x2 O 6 n - In 12 O 14 n – In 2 O 6 T – 12 In 2 O 6 n – 24 In 12 O 6 T + 12…

A: Definite integration

Q: + 8z7 – 5 sin z)dz O 4e -z +5cos z +e O 4e +z" +5sin z +e O 4e +z* - 5sin z +e O 4e +z – 5 cos z +e…

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Q: 25. cos² z dr CoS

A: Given that: ∫cos2x.dx

Q: 5. Evaluabe the following integrarls s sin thdz 471 ans2 3. Co sh 2 -277 dz ,c: 1 1 ans:

A: Your answer of First integral is not match my answer, either the expression of  integrand is…

Q: - In 2 | 2 e0 sinh 0 de - In 4

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Q: 1 Given that L-(4+9)) = 8in(Bt) – sin(Dt) L-'(+4)(s²+9) Match the following values. 10 is the value…

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