i) L-- (In) L- | s-3 6s+3 ii) L-1 iii) L(tet cos wt) s+1 sª+5s2+4,

Q: 10. Show that 2" + 42' + 8z = 0 if z = e-2=(sin 2x + cos 2x).

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Q: 10. Since (7,-1) is a point on f (x) cos z,which point will be found onf'(x) = cosx ? %3D O a (1,ח)…

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Q: 7. Prove that: (3) (a) (4) (b) sin20 cos20-1 in (-0) + cos (- 0) = cost -cote =

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Q: /2 1lf If In = " x cos" x dx, when n> 1, show that п(п — 1)1-2 — 1 In 12 [Hint: cos" x = cos²…

A: Given: In=∫0π2x cosnx dx

Q: Derive formula (2) on page 601. cosucos v 5lcos (u – v) + cos (u + v)]

A: Given equation is cosucosv=12cosu-v+cosu+v. cosu-v=cosucosv+sinusinvcosu+v=cosucosv-sinusinv

Q: 3. * S cos(3z)sin1º(3z) dz A 1 C (sin(3z))10 + C 3 (cos (3z))10 + C - -- В 1 (cos (3z))'1 + C 33 1…

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Q: Need help with explanation

A: 6) Solve the following:

Q: 1- , S" cos(x)esin(x)-8y dydx

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: (종-272 27=) + ain G + 272) The simplified form of cos O V3 cos 27z + sin 27z V3 cos 27z + v2 sin 27z…

A: Given cosπ6-27x+sin(π3+27x)

Q: -If u = x2 tan-1 २|४ y = - y² tan-1 x 22u дхду x² что - у² + J²u u ә2u u дхду дудх L ala 2

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Q: Prove: cosh 3x = 4cosh'x- 3 cosh x %3D

A: We will solve the following.

Q: 9) -135° Pos Neg Sin Cos -:-

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Q: 15. sin(2t + 글) dt = e2t-3 8. 7 4 7 64e3 7 4

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Q: Prove the following equation : Cosh(3 x) = 4 cosh³(x) – 3cosh(x)

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Q: 8. -dt 1+64t 2 sin-8 B. А. (). -1 2 tan 2 tan- 8 O c. D.

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Q: 4 cos z Evaluate S 16-y2 ydxdydz

A: To solve the given triple integral ∫0π∫04cosz∫016−y2ydxdydz…

Q: 5. Find all solutions of 2 cos x- -cos x-1 0 if 0sxs2n.

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Show that sin (2n + 1)z 2n +1 { 7/4 */4 0<まく

A: We will use complex analysis to solve the given infinite sum.

Q: Show that cos 3x = 3x has a solution in the interval [0, 1]. Hint: Show that f(x) = 3x – cos 3x has…

A: solution:-f(x)=3x-cos3xapplying intermediate value theoremintermediate value theorem states that if…

Q: 24. Evaluate: S(cos 2x) esin 2x dx A. -e sinzx + C esinzx +C C. esinzx + C esinzx D. + C В.…

A: using substitution method to solve integration

Q: Solve the problem from class: y'=y^(1/3) with y(0) = 0. How many solutions are there? How does that…

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Q: 5. Show that cos x = x has a solution in the interval [0, 1]. Hint chow that f (x) = x cos x has a…

A: Given, Cosx =x

Q: The simplified form of cos ( - 5z) 5z) + sin 6 52) + sin (; + 52) O v3 cos 5x + v2 sin 5x O v2 cos…

A: This can be evaluated as:

Q: sin(k/n). 1. cos(1) + 5/3. 2. cos(1) + 1/3. 3. cos(1) + 2/3 4. cos(1) – 1/3. O 1 O 2 O 4

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Q: 2π tane 13-12cose de

A: Given: The integral is ∫02πtanθ13-12cosθdθ. Evaluate the integral.

Q: 43. If |2| > 2, then f - dr r = fcos(5) + k B sin-'(5) + k: cosh-" (5) + k: Itanh-"(4)+k B 2

A: by using hyperbolic Trigonometry substitution

Q: ( 2 3 2 cos* 3 sin dx O (3/14) cos*7 (2x/3) - (3/10) cos^5 (2x/3) + C O (3/14) sin^7 (2x/3) - (3/10)…

A: Here, we need to find the integral ∫sin323xcos423xdx. So,                ∫sin323xcos423xdxLet…

Q: If 1, = |x" sin8x dx , Then 64 I,+n(n-1) I,-2 Select one: O- 8x" cos8x +n x" 7 sin8x O + 8x" cos8x…

A: Given :  In=∫xnsin8xdx                1 Using Integration by parts…

Q: v3 V3 sin 30 = , cos 30° = , tan 30° = COS %3D O sin 30° = , cos 30° = . , tan 30° = %3D %3D V3, cos…

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Q: 27. Evaluate: cos 2) - sin 6 4 /3 /2 2 2 1 V2 V3 2 2 1 V2 2 None of the above. + |

A: Hence option (c) is correct.

Q: 19. 2 sin 3x = V2 %3D 21. 2 cos (2x + 1) = 1 23. 2 sin (4x - 1) = 1 3x 25. 2 cos %3D EN =

A: The give trigonometric equation is: 2sin3x=2    ....(1) As we know that if the trigonometric…

Q: 3. tane de ) 71+ n cose)/3

A:

Q: я/4 4 sin (4t) dt. 9- cos (4t) Evaluate the integral я/4 4 sin (4t) dt%3D 9- cos (4t)

A: Use integration by parts

Q: Ti Ti to 8 Integrate cosh(4z) dz, C any path from - 8 Use the first method, if it applies, or use…

A: Using:- sinhx = -isin(ix)               Sin(-x)=-sinx               Sin (pi/2)=1

Q: 12. Write an éxpression that gives all sölutions to the equation. COS X - SIn x 3= 2.

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Q: 9 Prove Sen 4t 4 cos3t sint-sin3t cos t.

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Q: 2 7 4 is S cos' xsin xdx 비

A: See the details solution in below

Q: Compute sin (3r)dr (25z4+1)2 -

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Q: [² 11. [(2 sinx+cos.x) dx 9. 13. 15. x¹/3 19. 21. 3 x2/3 - dx 17. [(3 cos x - 2) dx [(5x- 2²/1) dx…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for you. If…

Q: if we let u-4x- 1 for the 2 tan(4x-1)-3 cos (4r-1) dx, what will be the resulting integrand? cos…

A: The given integral is  (2tan(4x-1)-3cos2(4x-1))/cos(4x-1).

Q: 11. One leaf of r = cos 30 12. One leaf of r = sin 40 13. Bounded by r = 2 cose %3D 14. Bounded by r…

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Q: neN JS E (4i +1) = 2n2 + 3n +1 n(n +1) . neN JI

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Q: 1 Evaluate | (x²sin y- xcos(y))dy O 2sin y-3cosy + C 6 -3sin y+2cosy +C 6 x2(1- cos(1)) – xsin(1) +…

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Q: Z {sin(3t + 2)} O (5 sin (3) + 2cos (3))/ (s^2 + 4) O (s sin (3) + 2cos (3))/ (s^2 + 4) (s sin (2) +…

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Q: 4 2 cos y + sen²y cos² y - senty 3 cos² y 1

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Q: L{sin(3t +2)} O(s sin (3) + 2cos (3))/ (s^2+4) O (s sin (2) + 3cos (2))/ (s^2 + 9) O (s sin (3) +…

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Q: 4.) Ž(1-sin1)* k=0 codh bs nohsrmotru betroupon or to lla bnit: I- 0pibcipojn BwGr p odmgon: 5.) n=2

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Q: 5. [(6+3z)cos(1+4z)dz 6. [2y° cos (9y)dy

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Q: f5cos(1-5x) dr = O - 5sin (1 – 5x) + C O -sin (1 – 5x)+ C 一 sin (1 5x) + C 5 - O sin (1 – 5x) + C…

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