lim ze = -9 cos 3 + i9 sin 3. %3D Select one: O True O False

Q: Write 2 cos(3t) + sin(3t) as Rcos(wt - ). |

A: Here we will write in the form of Rcos(ωt-∅),

Q: y = cot2(cos(θ))

A:

Q: 3. cos? (z) sin“ (2) dz

A: Given, The integral is,

Q: a) cosx = - ja 0 <x< 360° b) sin (2x +) = 0, ja - << c) 2cos?x + sin +x) – 1 = 0, ja 0 <x<2=

A:

Q: y= 6. 30 18/3/2 Sin(8)= Cos(8)D Tan() = %3D Sin(A)-

A:

Q: 2 y" + 4y = cos? x.

A:

Q: Evaluate du Form Answer 9 +p xp: r cos(Vx- 2) dx 2) sin (In/6*), -dx csc (3x) dx 16 - cot (3x)

A: This question has multiple parts, we are doing only the first two parts. if you want us to solve…

Q: Jo 17. cos² x sin? x dx

A:

Q: Solve for angles x and y of the following: (cos*2x – sin*2x) + j(csc²y – 1) = 0

A: The given problem is to find the values of angles x and y for the given complex equation. Given…

Q: If sin x - x sin x = -y cosx , then (y - 1) sin x = ? da C- x sip C+x sitft (B C - x COSX C+x COs

A:

Q: d²y If x=5+ cos20 and y=3- sin20, what is ? dx² A csc ³20 (в B - cot20 Ⓒ-csc ³20 D cot20

A: Given: x=5+cos2θ and y=3-sin2θ Now, dxdθ=d5+cos2θdθ=-2sin2θ and    dydθ=d3-sin2θdθ=-2cos2θ Now…

Q: 2. Sa cos x² da

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

Q: x² cos(6 x) dx

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

Q: (cos²x) y' = y²(y – 1)sinx %3D

A: cos2xy' =y2y-1sinxA first order separable ODE has the form of Ny·y'=Mx1y2y-1y'…

Q: Consider the equation below. 7 r = 6 + 6 cos(0)

A: Given equation is r=76+6cosθ

Q: OBTAIN THE GENERAL SOLUTION 1. X cos? ydx = + tan ydy

A:

Q: dr; 71+ cos² 0 csc? Od0; cos? 0 | (2² – |r – 1)dxr. -

A:

Q: If x = 4 sin 0, then J csc2ede = %3D

A: Here, ⇒x=4sinθ⇒sinθ=x4 By using Pythagoras theorem, We will have remaining side of the triangle…

Q: 10* -dx may be written as Aln secB*+ tanB* +C, where A, B, and C are constants not equal to zero.…

A:

Q: If cos A with A in QIV , find sec %3D a. sec | b. sec 2. с. sec A d. sec 4-5 %3D A sec e. A2 1/2 II…

A: Since you are asking multiple questions. We are answering only the first question. Given, cosA=18…

Q: az Find az and ду e = 5x 2² + sin(r + 2) – y?.

A: ∂z∂x=52xz2+2x2z∂z∂x+cos(x+z)1+∂z∂x…

Q: 12. y' = cos?x cosy %3D

A: Given differential equation is: y'=cos2 x·cos y Then we get, dydx=cos2 x·cos y Therefore the order…

Q: csc? a + sec? æ 1 cos x sin z

A:

Q: Simplify 1-cos(M)/sin(M) + sin(M)/1-cos(M) A. 2csc(M) B. sin(M) C. 2cos(M) D. tan(M)

A:

Q: 3. cos?wt

A:

Q: if y= 2cos (), then 을 A)-8cos (좋) B)-2cos (플) c) - sin () D Cos E)-올oos (즐)

A: If f(x) and g(x) are the function of 'x'  , then y= f(g(x))                 .............(1)…

Q: (a) sin(rxy) = x + y?

A: I am going to solve the given problem by using some simple caculus to get the required result.

Q: 10. y' + y cotx = 5ecos x, when x = 1, y = -4 ANSWER KEY: 10. y sin x + 5e cos x =

A: Please see the below picture for detailed solution.

Q: Pu Pu n. %3D dy? is cos (r – y) -3r sin (x – y) e (x+ y)? sin (x – y)

A: In these type of questions there may be more than 1 options. Check all the options.

Q: 11. cos (x) = sin (x + 20)° %3D I Answer:

A: We will use the trigonometric identity written below to answer this

Q: sec? e OP- Find Jo tan? 0+1

A:

Q: dy If x=5+ cos20 and y =3– sin20 , what is -? dr A csc 20 В cot20 none of the given choices -csc 20…

A:

Q: 16. Determine So sin x cos x dx

A: First simplify then integrate

Q: Write 2 cos(3t) + sin(3t) as Rcos(ωt−φ).

A:

Q: L" cos³ (;w) sin* (;w) dw -2π Se" cos3 Gw) CoS

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Q: T/2 *10 cos(8) r dr de

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Q: x = 4 sin? 0, y = 5 cos? 0 %3D in the given Cartesian form. with 0 <x< 4.

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Q: If I = 4 sec46(x) tan138(x) dx uP (1+u2)9 du , then %3D a = b = p = = b

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Q: dy -? If x=5+ cos20 and y=3– sin20 , what is dx A none of the given choices B csc 20 (c) -cot2ө D…

A:

Q: dy If x=5+ cos20 and y=3- sin20 , what is -? dx (A) cot20 (B - csc320 © none of the given choices D…

A:

Q: b. sin? () = 2 over [0, 2n) %3D

A: EXPLANATION

Q: the value of (yn)o If y= Sin (msin , find

A: Given that We need to find the value of

Q: Evaluate  -3 to 3 ,  0 to (9-x^2)^1/2   and  ∫∫sin(x^2+y^2)dydx.

A:

Q: de I cos? 0 2

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Q: dx = ? 4 sin x – 3 cosx+5

A:

Q: 2 55. y = cos(-)

A:

Q: 10 -dx may be written as Aln secB+ tanB*+ C. where A, B, and C are constants not equal to zero.…

A: Given: I=∫10xcos10xdx   We know that; ∫secxdx=lntanx+secx+C   So, we can also write as;…

Q: Find the volume

A: Given

Q: V3 4) cos(20) = 1 2 %3D

A:

Q: b. Sina 142 ヒ (os142 t cos? F. Sin go° + (05290°

A:

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.