2 L- e3s [(s + 2)4 + 13(s + 2)² + 36] ,-31+6u(t – 2) sin(2t) sin(3t) 3 2e-31+6, u(t – 2) sin(2t-4) sin(3t–6) 10 15 2e-21+6 u(t – 3) sin(2t-6) sin(3t-9) 10 15 2e-21+6. u(t – 3) (sin(2t – 6) – sin(3t – 9)) 30-3t u(4 ?) ||

Q: 2. L- e3s [(s + 2)4 + 13(s + 2)2 + 36] ] sin(2t) 3e-3 u(t – 2) ( * sin(3t) 2e-2' u(t – 3) (…

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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: L-1{3{8+1) – 140) (s + 1)² + 400 J e-t(3 cos(20t) + 7 sin(20t) e-t(7 cos(20t) + 3 sin(20t) Option 1…

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Q: |(4e + 5z* – 3 sin z)dx- O 4e² – x³ +3 cos x + c O 4e? +x³ +3 cos x + c O 4e² +x³ - 3 sin a + c O…

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Q: -4 -2 (a) x=¹t+3, y = 2² VX (b)x=²2t, y = √t 11 (c) x = ²³ - 2t, y = 2² - t ✓X III (d) x = cos(5t),…

A: Please see the below picture for detailed solution.

Q: 2- S x. Sin (5X) dx : Cos (SX) Cos (SX) Cos (SX) XSin (SX) XSin (SX) 25 25 25 P+9 P+9 P-9 3- L{e.…

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Q: 3. The value of A. B. C. D. [xsản xdx (1 - x²) 3/2 + C -sin-¹ x - √1 − x² + ² - (1-x²) ³/² + C sin-¹…

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Q: 27. f"(1) = 12 + sin 1 28. f"(t) 29. f'(x) = 1 + 3x, f(4) = 25 30. f'(x) = 5x- 3x? + 4, f(-1) = 2…

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Q: 10 L-1 e2s [(s + 3)4 + 13(s + 3)² + 36| sin(2t 글e-3+0u(1-2) (Mn2 sin(3t)) - 2e-21+6u(t – 3) (sin(2t…

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Q: 2 WWw -21 2T -TT TT -2 -4 -6 s(2) = 3sin(x + )-2 f(x) = 3 sin x + 4 A) f(x) = 3 sin 2x + -2 B) f (x)…

A: Please go through the attached solution.  Thankyou . Best regards.

Q: 4 Se + 5x* + 10 cos x + 2)dx 5e" + x° + 10 sin x + 2x + c 5et + x 10 sin x + 2+c - et x° + cos x + 2…

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Q: 3i +2V2 - 5n -4i +6(1 +a T/4 [(3sec2 t)i - (5 + sin t)j - (6sec t tan t)k)]dt Find 0. 2 2-57T-4 3i +…

A: ∫sex2xdx =tanx+c∫(constant)dx=x+c∫sint dt =-cost +c∫sect tant dt =sect+c tanπ4=1cosπ4=12secπ4=2

Q: 10 L- e2s [(s + 3)4 + 13(s + 3)² + 36] sin(2t) e-3+6 u(t – 2) sin(3t) 3 sin(2t-6) 2e-21+6, °u(t – 3)…

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Q: 15. y=x6 18. y=sin(2x-л)+2 15. 16. A. 10 8 6 4 4 D. 3 laten each glapn will а -2 2 0 -2 -4 2 3 16.…

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Q: 1. F (x) = sin x+ 2cos x – 5 %3D 2. G(x) = 3e* – 7log;x – 2 * 3. H (x) = 4sec x + 5tanx 4. Z (x) =…

A: Since there are multiple questions. We will solve only the first three questions. If you want to…

Q: cOs x dx |(sin? z + 4)%/2 1 sin x sin x cos x 1 cos x +c +c 16 vsin ²x + 4 48(Vsin ²x + 4 16 Vsin 4x…

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Q: 7. y = cos`x sin'x %3D 3 A. – 4 cos x sin x B. – 2 sin sin 2x 3 2 C.- 4 cos´x + sin' D.- 2 sinx cos…

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Q: f(t) = e^3t - cos(6t) - (e^3t)(cos(6t) * O F(s) = 1/(s-3) + s/(s*2 + 6*2) - (s-3)/(s*2 - 6x + 45) O…

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Q: 7. y - 5y"" + 7y" - 5y' +6y=x² + 3x - 5 Ans: y = C₁e³x + C₂e²x + C3 cos x + C4 sin x + x² + ²x - 3/4

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Q: sin(8t) -2t O a. r(t) = e cos(8t) +e2t O b. x(t) = e 4t cos(8t) – e t sin(8t) COS O c.(t) = e2t…

A: Given,         dxdt=12x-8y        dydt=16x-4y

Q: | (4e" + 8x" – 7 sin x)dx O 4e* + x8 + 7 sin x + c O 4eª + x³ – 7 sin x + c O 4e – x8 +7 cos x + c -…

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Q: (4e" + 5x* + 5 cos x)dx 4e" + x + 5 cos x + c O et – x + cos x + c - O et + x5 – 5 sin x + c 4e" +…

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Q: 8s+12 F(s) %3D s2+4s+29 a. f(t) = 8e2t cos 5t –e2t sin 5t c. f(t) = 8e2t cos 25t –e2t sin 25t %3D b.…

A: We need to calculate the inverse Laplace transform of Fs=8s+12s2+4s+29 Now, s2+4s+29 can be written…

Q: -3u Let z=sinh-(y-2x), where x = we and y3= dy3In then is given by ди OA -3u 6we 3u 1- (y-2x)2 В.…

A: Note: We are entitled to solve only one question at a time. As the specified one is not mentioned so…

Q: 2 L- e3s [(s + 2)4 + 13(s + 2)2 + 36] 3e-3* u(t – 2) ( antzn sin(2t) sin(3t) 3 sin(2t-6) 2e-2' u(t –…

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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: (-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: 2.* 3 S(x* + 2x - 1) cos 4x dx 3x2 +. 16 13 х 13 sin 4x + 4 cos 4x + C 32 128 B 13 х (3x2 sin 4x + 4…

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Q: L- [(s + 2) + 13(s + 2)2 + 36] e u(t - 2) ( sin(2) sin(3r) 13 2e 6 u(r – 2) ( in(2r-4) sin(3r-6) 15…

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Q: -2s+9s2-8s+18 Find L-1 s(s²+4)(s+1) O (2- 5e +3 sin 2t) O (3 - 5e-t + 3 sin 2t) O (1-3e-t +3 sin 2t)…

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Q: L{3e2tsin4t – 4e2"cos4t} 16(s-2) (s-2)2+16 4(s-2) a. (s-2)²+16 3. b. (s-2)² +16 12 (s-2)2+16 4(s-2)…

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Q: /² sin sin ( π/4 x² dx (x²+4)5/2 (Use trigonometric substitution) fe2x+Inx² sin x² dx = = Find f…

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Q: A. x + 2 4. x² + 4x + In (x + 2 + Væ² + 4x) + C 2 2 x + 2 4 x + 4 -1 x' + 4x sin -) + C 2 - 2 2 С.…

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Q: (). %3D e2(s-6)²+25)) u (t – 2) (cos 5t + sin 51) O u(t – 2)et cos(5t – 10) ,6t | - u (t – 2) er-12…

A: We will find out the required value.

Q: d2s 2= -162cos (9t), s '(0) = 9, s(0) = 8 dt2 A) s = -18 sin (9t) + 9 C) s = 2 cos (9t) + 9t + 6 B)…

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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: 5s s+4 s2 + 16 -f(t) 3e 4t-5 cos 4t C. f(t) = 3e¬t - 5 sin 4t .f(t) = 3et-5 cos 4t D. f(t) = 3et - 5…

A: Given Laplace transform is F(s) = 3s + 4 - 5ss2 + 16

Q: Express as a product a. cos 5t + cos 6t b. cos x + 2x

A: We have to express as a product  (a)  Cos 5t + Cos 6t We know that  CosC + CosD =…

Q: Finding a Viewing WindowIn Exercises 11–30, find an appropriate graphing software viewing window for…

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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

Q: 2² sin(1/2) z 7 0, f(2) = z = 0.

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Q: 7. (D + 4D² + 4D)y = cos x 4 a. y = C, + Cze-2* + Czxe¬2* . 25 cos x+ 75 sin x 4 b.y = C, + Cze¬2* +…

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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: f() = Sin - 2 <u< -/ (9) ○テkラ1- 一2 -1 2. b) f(x) = t ? An cos (NTTX) + E Bn SinntIk ニし Ao Ao = ー2 ー2…

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Q: x²+2x 1. S**** is equal to x+1 c. +x + In\x + 1| +c 1 А. х — + C С. 2 1+x x2 В. 2 D. -+C 1 + x –…

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Q: ( S L-1 e2s ( (s-6)²+25) u (t – 2) e6 (cos 5t + - sin 5t) O eor (cos 5t – sin 5t) и (1 — 2) е-6г…

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Q: 2 tan (4x – 1) – 3 cos?(4x – 1) cos (4x – 1) If we let u= 4x -1 for the integral of dx, what will be…

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