y = arctan 2x -16x 16x (1+ 4x2)2 (1+ 4x)2

Q: Find a result by using undetermined coefficients for ý + y = x² + x+sin(2x)

A:

Q: S Find sec42x -dx tanº2x cot²2x-cot82t+C 12 16 1 1 1 1 12 tan 62x 16 tan 82x --(cot$2x) (² 1+3csc²2x…

A:

Q: 3x y= + Arccos () V8-x3

A: See the details solution in below

Q: Find y': y=- Vx* + 4

A:

Q: - sin² ydy 6. 4 tan" y

A: As per the guidelines I can solve only first question

Q: Differentiate y = 5x° – sec¯1 x -

A:

Q: S sec²(4x)(3 – tan(4x))³dx

A: Given integral is ∫ sec24x3-tan4x3dx.

Q: 1 2. y = arctan 2 2(x2 + 4) -1 3.. y = 4 coth(9x – 3) |

A:

Q: 9x² + 4x + 6 dx 2 9x² +1

A: The given integral is (9x2+4x+6)/(9x2+1).

Q: 2Cos3xSenx +Sen2x Simplificar: E= %3D 2Cos7xCos3x- Cos10x

A: Given E=2cos3xsinx+sin2x2cos7xcos3x-cos10x To simplify this the identities used are…

Q: り plot s XE[-2T,27] Sin3X „Cas2X,

A: a.  Given function is, f(x)=e-x2 We find that f(0)=1 and when x→±∞, f(x)→0 So, the graph will be,

Q: (4D2 + 4D + 5)y = 40e−3x/2 sin 2x

A: Given that, 4D2+4D+5y=40e-3x2sin2x

Q: the domain of y=Sin3X is

A: The graph of the function y = sin 3x is as shown below:

Q: 3) (x²D² - 2xD+21)y=x³ sin

A:

Q: y = sin(3 – 4x)" %3D

A: Apply the chain rule of derivatives, If y = f(g(x)), thendydx=d(f(g(x))d(g(x))×d(g(x))dx

Q: x – 5y = -4x - 2y %3D II at x -3.

A: Simplification of the equation helps to find the required function value. Substitution of the point…

Q: y = arccos /1 – x (1-x) 2 1 (1-x) 2 2 JA (1–x) 2 1 (1–x) 2

A:

Q: y=2(21,2-1 + arctan x) 2 2 x-1

A: Please see the whiteboard.

Q: 4)y = 2 sin (3x +) - 1

A: Given: y=2sin3x+π5-1

Q: Evaluatef (cot2x + 2tan²x - 5) dx a. cotx + 2tanx + 4x + C b. -tanx-2cotx - 4x + C c. -cotx 2tanx -…

A: I have stated the used formulas in the solution

Q: y" + 9y = sec 3x %3D

A:

Q: If y = (x+1)/(2x - root x' then y' will be?

A:

Q: y = 3Arcsin (2x³) -- Arccos(2x³)

A:

Q: Solve (D² - 2D + 5) y = sin (2x) + 17x cos (2x) — 15x -

A:

Q: sec?x - dx |1- 4tan²x 1 –

A: We will solve this question using simple Integration formulae.

Q: If arcsin(6x+4y) = 1.5708 and arccos (2x+y) = 1.0472,find x.

A:

Q: Differentiate y= 7^(x)-3sin(arctan(5x))

A: Solution: The objective is to find the derivative of the given function

Q: 2) Sketch: y = -x(x + 50)(x – 1000)(x + 1)

A:

Q: y=3x^(3/2) on [2,4] find arclength

A:

Q: 3. (2x2 + 2)dy + xydx = 0

A: (2x2 + 2)dy + xydx = 0

Q: 5x dx (4 + x²)²

A: Follow the steps.

Q: 8. y = x ¹ Arctan 4(x4)

A:

Q: . y = 3Arcsin (2x³) -- Arccos(2x³)

A:

Q: 식을 증명하여라. x -1 -= 2arctan vx- x+1 arcsin 2

A:

Q: What is the of y = (tan-¹4x)² ? 2 - 2tan ¹4 1+16x² 1 8tan ¹4x 1+16x² 2tan-1 ¹4x 1+16x² -1 8tan ¹4x…

A:

Q: Does x2 - 10 = x sinx have a real solution? Show your process. -

A: Let f(x)=x2-10-xsinx  Then it is clear that f is a continuous function on R. Now…

Q: ydx + 2(y4-x)dy=0

A:

Q: Differentiate y = x'arctan 2x 2x A. 1+4x2 - 2x arctan 2x 2x3 В. + 2x arctan 2x 1+4x2 C. 1+4x2 + 2x…

A:

Q: Sketch Z= 2x^2+3y^2

A: To sketch: Z=2x2+3y2.

Q: Evaluate the following integrals

A: The given integrals are,

Q: y = Arctan 2+x 1-2x

A:

Q: Integrate the fallowing. 3X Cosaxd X

A: Integrating by parts∫(I).(II)dx=(I)∫(II)dx-∫∫ddx(I)∫(II)dxdx

Q: 91 182x-x2 9V x²+y² dydx %3D

A: Here we solve double integration problem.

Q: y"'-2y"= tanx

A: We solve this by using the power series. We expect the solution to have a power series expansion…

Q: sec. sec A x2 + 1 x2 +1 2x Option 1 Option 2 x² – 1 x2 – 1 - 2x Option 3 Option 4

A: Given secA+tanA=x To find secA:

Q: y = (x – 1) 2x – x² + arcsin(x – 1) %3D - - - O - 12x – x² O - 2/2x – x² O V2x – x2 O 2v2x – x²

A: How to find the derivative of the given two functions.

Q: 3x dx | sec 2

A:

Q: 9 y= Arctan( 1-2x

A: Use simple differentiation twice to get the answer.

Q: V8 -x² 2 (x² +y²) dydx

A:

Q: 5- y = 1+sin(4x2 + 2)

A: Note - As per our guidelines we will solve first question only and rest will reposted.  ddxxn =nxn-1…