.csc(2x + :-2, where x € ( =) 4 - sin? () + cos²x = 1,where x € [0, 21) %3|

Q: 3. S sin®2y · /cos2y d|

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Q: Si sin“ (3y) cos® (3y) dy 128 2340135 128 780045 O 9.64 x 10 4 O 2.89 x 10 3

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Q: (D² – 5D + 6)y = 15 sin x – 15 cos x - -

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Q: Solve the following equation; 2 tanh- 2r = In(r – 2) – In(x). %3D

A: We solve this following equation using simple mathematics and its solve in a simple form of…

Q: Solve the fllowing D.E +4y= cos x - sinx 2. CoS X %3D

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Q: O. p. S sin 2x cos 3x dx 3dx /1 + 9x²

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Q: 18) e2x = sin(x + 3y)

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Q: (a) In(1– x) +xe? (b) 2х 2x 1-cos(x) (d) V1+x-1 Check and briefly explain how to avoid the loss of…

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Q: The f sin x cos x dx is not equal to {A} -cos 2x + C {B} sin²x + C {C}-{cos²x + C {D} sin 2x + C

A: A detailed solution is given below

Q: a) y = sin x² cos 2x 4.

A: Given: y=sinx2cos2x, y=cos4sec23x We know that ddxuv=vdudx+udvdx…

Q: Find: O d: x-6,X-1 dy 3 23=Sin (cos 8x)

A: 1 .y=45x3-6x2+x2-12. y=sin(cos(8x))

Q: establish each identity.

A: Given  The identity is ln sec θ=-ln cos θ

Q: To evaluate 3cosx -1 1- sin?x dx, the integrand can be transformed to A J(3 cos x - sec²x) dx ® S(3…

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Q: If h (x) = cosxdx and h =4, then h (0) is equal to

A: answer is in step 2

Q: L(cos at) = s2 - a2

A: To verify that ℒcos at=ss2-a2.

Q: L-1 (s² + a²y² (sin at + at cos at] 2a

A: Some of the properties of the inverse Laplace transform L-1aF(s)+bG(s)=aL-1F(s)+bL-1G(s)…

Q: Find the smallest positive solution of cos x = eX; x0 = 1 by iteration.

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Q: Evaluate the integrals in Exercises

A: Question 7 - Let the given integral be y - y = ∫lnx-5x-5dx       ............(1)Let,t = lnx-5…

Q: (a) Show that cos(x²) > cos x for 0 ;. 1

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Q: , Sercoszx *cos2x dx 3.

A: Since multiple questions are asked answering the first question, repost other question for solutions

Q: 1(y) = In(sin(cos(y²))) %3D

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Q: (d) lim In(cos r) エ→0

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Q: Suppose m and n are constants and m #n. Evaluate sin(mx) cos(nx) dx-

A: To evaluate we first multiply and divide by 2 the given function.  Then use the formula: 2(sin(mx)…

Q: ex sin(e*)dx 8+cos²(e*) (x+2)dx x2-3x+5 dx -2 x²+4

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Q: Given In = S cos" x dx = - cos"-1 x sin x + In-2 ; %3D n/2 determine a reduction formula for cos" x…

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Q: The integral So (cos(3x))² sin(3x)dx under the change of variable u = cos3x becomes - ov 29 9/29 u?…

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Q: IFS(x) = - sin(x), then S ® (1) is equal to - sin(x) B) - cos(x) sin(x) O cos(x)

A: We have to solve

Q: 2 cos(플x-지) =D v2 TO

A: Given trigonometric equation is:  2 cosπ2x-π=2 We have to solve for x.

Q: Solve the following for 0 s x s 2n. cotx cos² x = 2cotx

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Q: too ·00 dx COSX x² +hx+5 =le Residue solution cos (2)

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Q: Find the solution of the following problem accurate to within 10-5 using the Secant method. In(x -…

A: Secant method is one among different methods used to approximate the zero of a function within an…

Q: Use the reduction formulas from problem #2, to integrate the following: a) | cos* (3x) dx

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Q: For | cos 3x cos 4x dx :

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Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

Q: 1 dx 3 sin x+4 cos x+3

A:

Q: Find the solution of the following problem accurate to within 10 using the Secant method. In(x – 1)…

A: Given function is ln(x-1)+cos(x-1)=0 and 1.3≤x≤2 So f(x)=ln(x-1)+cos(x-1) Let x0=1.3, x1=2 So…

Q: 4. J S (esc²a – co sec 0 tand) d0 - -

A: Explained below...

Q: 4) Evaluate the following sin (x) -dx 1+ cos (x) 1 ex dx (4x³ + 7*)dx --

A: Consider the following integral: I=∫sinx1+cosxdx Substitute 1+cosx=t→-sinxdx=dt→sinxdx=-dt in I:…

Q: Find the solution of the equation =e* cos y hich tends to zero as x - 0o and has the value cos y…

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Q: S cos(nt)dt

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Q: Q1:- Solve the following DEs:- ху?-cos x sin x 1) y' У(1-x?) 2) (-4y + e-3*)dx = 4 dy -Зх dy 3) +…

A: We have to solve the given differential equation Here I am giving answer of 1st question if you want…

Q: "+25y 4r sin(51) – 2e" cos(5t)

A:

Q: -3 cos (2x)+sin(2x) in the form Rsin(2x+a)where R>0 and 0 <a<2n. Express

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: The result of solving the integral x' tan(x²) dx is: A) Inlcos(x) +c B) tan(x)-+ In/cos(x²)|+c D) +1

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Q: d²s dt2 sin 3t + cos 3t |

A: In this question, we need to find s.

Q: 1 Evaluate the equation /o x² sin (xy)dydx

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Q: dy.xandy in =cos = COS e

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Q: 3 Differentiate: y = In cosh° (cos 2x)

A: As we know that: The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1 From the given problem:…

Q: Find the general solution of the DE: dy/dx = sin(7x) cos(5x) + cos(7x) sin(5x).

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Q: Evaluate D°(cos x+e-2*) (A - cos x +64e -2x B - sin x – 32e -2 cos x – 32e-2 D sin x +64e -2x

A: Explained below