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

Q: (a) cos(iz) = cos(iz) (b) sin(iz) = sin (iz) for all z; if and only if z = nлi (n = 0, +1, +2, ...).

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Q: cos-1 3x dx 3 – 1 – 9x2 * tan-1x dx 1+ x2 4 - n/2 5 –

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Q: ЗсoshЗx dx| 4 + sinh3x 1/3

A: Given: 13∫3cosh3x4+sinh3xdx

Q: ed 1+ 2! Bn(0). (2.59) 3! n=0 Comparison of the powers of A gives lo(0) = 1, B1 (0) = -12, B2(0) = ,…

A: Given λeλ-1=1+λ2!+λ23!+...-1=∑n=0∞λnn!Bn(0) if we take L.H.S.…

Q: 2n sin(30) do 4. Jo 5+cos²(0)

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Q: 1 L-1 s(s² + 4). 1 1 [1+ sin(2t)] 2 [1 – cos(2t)] | Option 1 O Option 1 1 1 [1+ cos(2t)] 4 [1 –…

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Q: 1 15. sin(re) = ; dr then ep a) cose (b) (c) 등 (d) 등cos'e

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Q: 14 :Q13 (-9)" (2n)! (a)e (b) cos 3 (d) sin 3 (e) None (c) cos a b C d. e

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Q: 1 – s2 S

A: we have to differentiate y  y=cos-1s+s1-s2

Q: Evaluate answer = 5 5 cos(x) ln(1 + x²) + x4.6 1+ el.63x-66.3 dx.

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Q: dx 2. √ 9x² + x³² 12.

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Q: 23. fx² sin 2x dx is a. b. x² cos 2x -x sin 2x-cos 2x + C x² cos 2x -x sin 2x + cos2x + C -x² cos 2x…

A: Given problem:-  ∫x2 sin(2x) dx

Q: limtt 2 +z+1

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

Q: Q7: True/ False (t? cos 4t) = L(t2)L(cos 4t).

A: The solution is given below:

Q: 19. cos (20) 1/2

A: We will find the value of θ in the following step.

Q: 2. L{sin² = nt} 7² a. S³+π²s π² b. 772 2s3-2π²s π² C. 772 2s3+2π²s π² d. S³-π²S

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Q: What is L 2. s² -7 s -36 cosh 3t +sinh 9t 3. B. cosh7t +sinh 6t C. 5cosh 10t + sin 2t D. s 31 +sin…

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Q: 6x-7 4. S (2x+1)(4x²+1) dx In(4x² + 1) – 2 In(2x + 1) -Tan" (2x)| + C'

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Q: (sin 4z + cos 4) O 2+ sin 4I COs 4r O 1+2 sin 4x cos 4x O 4+ sin 4I COs 4x O 1+2 tan 4x cos 4x O 1-…

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Q: tan (x)dx = %3D O None In 2 /3 - *+ In 2 4 글 In(을) TC 6/3 - In 2 /3 - In 2 || 4

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Q: And periad of :- yatan 4x @ yosco 5 Cos 10X 2) "Q2 S Ske kch these famckan g- these fanction g- L ye…

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Q: 1) y = cos (48 + 11)+1 1 2 6

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Q: -2x xp- (1-x)' 7. Evaluate A. +6x-n(1-x)+-(1-x)* +C C. '+6x + n(1-x)' + (1-x)*+c D. x+6x + In(1-x)"…

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Q: L{3e' sin(5t)} 15 +25 52+25 (8-1) +25 15 $2 28+26

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Q: dx √(1-x²) 7. The value of f A. CONNE Oc O J. N is B. sin '(x) + c 4 C.rosx + le D. cosx A 8. Jcos'…

A: I am attaching image so that you understand each and every step.

Q: S(x + 2) sin(x² + 4x – 6)dx

A: Let I=∫x+2sinx2+4x-6 dx

Q: 6. 7. 3+6s+45²-25³ s² (s² + 3) 26-5²- s(s² + 4s+13) [2+1+√√3 sin √√3t-4 cos √√3t] 2 [2-3e-2t cos 3t…

A: To find the inverse laplace of the following.6 3+6s+4s2-2s3s2s2+37 26-s2ss2+4s+13