1 - / sin2r - ycos2r điferansiyel denkleminin genel çöztumt aşağıdakilerden hangisidir? a) Hiçbiri b) O y=c v sin(2r) c) y = -2V sin(2x) +c d) y = sin( 2x) +c e) sin(2x) +c

Q: 3. The integral of sin24x cos4x dx is a. (1/4) sin³ 4x + C b. (1/3) sin³ 4x +C c. (1/12) sin³ 4x+ C…

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Q: Prove that 1-x ', V 2 1+x cos'x = 2 sin 2cos 2 COS 1 -1

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Q: 3. Differentiate. SET A. y = 3 cos(5x2 + 2)

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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: Use a change of variables or Table toevaluate the following definite integrals.

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Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

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Q: Use a change of variables or Table toevaluate the following definite integrals.

A: Given:  Calculation:  Let ln(p) = u Differentiate both sides (1/p)dp = du Also the limit of…

Q: What is the integrable form of sin-cos-sin0 do? 2 2 (A) 1- u² du B - 2 sinu du u² – 1 du 2 cosu du

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Q: * DeMoivre's Theorem 4 (4(os 30 + ) i sin 30

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Q: 5)Prove that (1+sinx)(1+sin(-x)) = cos²x (manipulate left side in order to get right side) %3D

A: We have to prove the given identity: 1+sin x1+sin -x=cos2 x We know that sin -x=-sin…

Q: tan u du = In | sec u| + C

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Q: () TT sin TT 31. sin 32. cos cos 33. sin sin 4 34. cos cos 35. сos -1 cos 36. sin sin 6. 6 (c() 37.…

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Q: using De Moiuve's theor@m, show Tsat sin50 = 16 sino -20 sin o + 5 sin o ニ Hense salve z4 K -30%+ Ex…

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Q: The integration expression + 4)cos(3ln(x) +4)dx must be transformed into using suitable choice of…

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Q: Place these trig equations into general form: 1. y = sin (4x + 3π/2) + 2 2. y = cos (3x - 6/7) 3.…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: e cosl – i e™ sin 1 + e¯ cos 1 - i e- sin 1 2 e cosl + i e™ sin 1 – e- cos 1 + i e¯I sin 1 -TT 2 e…

A: Simplify the given expression: Coshπ-i

Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Prove | cosz |2 = cos²x+ sinh²y.

A: To Prove: cos z2=cos2x+sinh2y

Q: 1 sinx # 1-cos2x ẩu! (6 2

A: Given query is to find the value of the limit.

Q: If Y=tanx prove that %3D2

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Q: how that cos 1+cos 8 and sin 1-Cos 0 %3D %3D using de Moivre's Theorem.

A: It is required to show that cosθ2=1+cosθ2 and sinθ2=1-cosθ2 by using de Moivre's theorem. By de…

Q: prove that. sinh ciz) = i sinz sinciz) zisinh z , cescia)= coshz

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: Evaluate 1¹ 1 - cos 2x sin 2x dx In | csc 2x + cot 2x | -ln | sin 2x | +C In 1|csc 2x-cot 2x |--In |…

A: The given integral is: I=∫1-cos2xsin2x   As we know the common integrals; 1). ∫cscxdx=lncscx-cotx+C…

Q: Use Table to evaluate the following definite integrals.

A: Given: ∫0110xdx

Q: 1)f sin 4xdx cse(2+3lnx) dx 2) fcos 2xdx 7)f sec (4x)dx 3) fx tan(2x2 +1)dx 8)fx csc| 3- dx 3 dx…

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Q: 3. On (-∞, ∞), three functions y₁ (x) = cos 2x, y₂(x) = sin² x, y³(x) = cos² x are linearly…

A: Note: As per the guidelines we are supposed to only one answer because this is not a subparts…

Q: What is r 1- O Option 1 2 2 sin 0-3 cos 0 3 y = ² x + 1 2 x² + y² = 2y²-3x Option 3 in Cartesian…

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Q: Use a change of variables or Table toevaluate the following definite integrals.

A: To evaluate: ∫0π2sin2θ cosθ dθ Solution: Let substitute t=sinθ dtdθ=cosθdt=cosθ dθ Limit will also…

Q: 1 a. Simplify cotx secx CSCx) 2cotx C. secx +cscx cotx С. secx cscx d. secx +cscx cotx d. cotx…

A: (A) We have given cotx·1sec x+1csc x=?   Simplifying it We get cotx·1sec x+1csc x=cotx·csc x+sec…

Q: 13. Differentiate 1 3 y = 2x2 + 6x3 – 2x2 а. 2 6 b. у 3 —t 4 3 x2 3 x4 x2 'x3 y = sin³ [cos(tan(3x –…

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Q: 1) y = 3sin(x) 2) y = 2sin(3x) 3) y = cos(-)

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: Find y' where y = 8 cos-1 (sin (19 z)) – cot-1 (14 z) Answer: 14 y' = -152 1+196 z2 -152 cos(19 z) +…

A: This question belongs to derivative of inverse trigonometric function.

Q: 9-10.j Show that sin20 2tane %3D 1+tan20

A: We will prove the trigonometric formula.

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: Evaluate: Scos 2xdx cos2x, cos 2x +C A 2 6 sin2x sin32x +C 6. B 2 cos2x cos 2x + C 6. 2 sin2x,…

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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: Use a change of variables or Table toevaluate the following definite integrals.

A: The given integral is ∫04p9+p2dp. Let x2=9+p2. This gives  2x dx=2p dpxdx=pdp. when p =0,  x=3. when…

Q: The suitable substitution to evaluate the integral cos°(2x) dx is 5(2x) 3 csc°(2x) u = sin(2x) u =…

A: First, simplify the integrand and use the substitution method

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: Use Cramer's rule to solve for x' and y' in terms of x and y. x = x' cos 0 – y' sin 0 y = x' sin 0 +…

A: Solution is given as below:

Q: Given: z = sin 3x cos 4y Find: z ду2 -3 cos 3x sin 4y -9 sin 3x cos 4y -12 cos 3x sin 4y -16 sin 3x…

A: Differentiate the given function partially w.r.t y keeping x as constant   ∂z∂y=sin 3x×4-sin 4y…

Q: 7.2 (A) 1. S sin x dx cos x + C because(-cos x +C) = %3D dx 2. S cos x dx = because sin x 3. S tan x…

A: We need to solve the given integral. This can be done as follows:

Q: 30 csc (3x) cot(3x) dx (Use Substitution Method) 30 30 + C 6 cos² (3x) 6 30 30 + C 6 sin²(3x) 6 30…

A: Given that  I=∫ 30csc23xcot3xdx We need to substitute the appropriate value so we can solve it…

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: cost+cos4t+cos7t / sint+sin4t+sin7t = cot4t

A: SOLUTION-

Q: 11 csc²(3x) cot(3x) dx =, (Use Substitution Method) 11 11 +C 6 sin (3z) 6 11 11 +C 6 sin (3z) 6 11…

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Q: Let w- fx.y.) - :), x- cos(), y sin(» and :. Then:

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Q: 26 csc (2x) cot(2x) dx (Use Substitution Method) 26 26 + C 4 sin (2x) 4 2 26 26 + C 4 sin? (2æ) 4 26…

A: Integration.

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: Given     ∫(x+1)42xdx Formula ddx(xn )=nxn-1 ∫xndx=xn+1n+1+C

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.