[ arctan (1-x)]² 4x2- 8x+8

Q: Iim tan³x X10 1- Cos2x

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Q: 2 cosx+3 cosx=2, 0Sx<27

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Q: -y 2 Sec-x ес

A: 0xGiven function y = 2sec(1/4)x and period = π/b

Q: Sec2(3x)=4 in the interval [0,2pi]

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

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Q: x V16 x2 1. y = 8 arcsin 4 - | 2 1 2. у arctan 2(x2 + 4)

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Q: cos-1 3x dx 1- 9x2 3

A: Answer

Q: [xVtan x² sec* x² dx -

A: Given,         ∫xtanx2sec4x2dx

Q: 9x dx VI-9x -/1-9x2 +C -1 arcsin 3x + C + C 3(x3 – 3x)

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Q: Find y' and y". y=2sin4x-cos(8x-1)

A: Let's find.

Q: x5tan(x²) sec²(x²) dx

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Q: q-Sin ²1x1 1²/x/_alx

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

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Q: y= - 2 cos 4x +3

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

A: Please see the whiteboard.

Q: 5tan 2x -dx- sin22x-1 8.

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

A: Given: y=2sin3x+π5-1

Q: 2x+5 dx = AV7- 6x - x2 + B sin - (**)- 1. Vア-6xーx2 +C

A: ∫2x+57-6x-x2

Q: csch (2 sin2x)dx 1. 1– 4x²

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Q: 4. f(x)=x tan² (-)

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Q: In(arctan(x)) da 1+ x² 1

A: Given that a integration and we solve this integration by using general formula of integration.…

Q: f(x) = sec-'(1 + x²)

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

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Q: Solve for Fourier coefficient, f (x) = Ssin x 02x2n T >x 22n

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Q: f(x) = x² sinh (3x) - %3D

A: Find f`(x)

Q: Solve for x if Arctan ( 1 – x ) + Arctan ( 1 + x ) = Arctan ( 1/8 ).

A: Given: arctan(1-x)+arctan(1+x)=arctan(18) We have to solve for x

Q: ( csch (2 sin 2x) dx V1-4x

A: We have to find indefinite integral

Q: 8. y = x ¹ Arctan 4(x4)

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Q: .2 x² arctan(3x) dx %3D

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Q: sec x tan x dx 9+4se ²x 2.

A: We have to evaluate the integral: ∫sec x tan x9+4 sec2 xdx Solving the given integral by…

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

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Q: 2Cos 2x- Sin20-2

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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…

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Q: 3 (x) - 128 (sin4x)+ -1054 (S/8x) | 60

A: We have to answer following Questions.

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: 2. Sin 2x dp X UIS 6.

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

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Q: sec2 ) 15. Evaluate. - x2 dx

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Q: 12) (Vy)* = sec-1 (x)

A: The detailed solution is as follows below:

Q: 6) y = cos-1 (9x2 – 4) V1 + (9x2 – 4)2 -18x C) V1 - (9x2 – 4)2

A: Given function, y=cos-19x2-4

Q: sec²(/x) dx 38.

A: According to the guideline we should have been able to solve only one question at a time #38

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: )Evaluatef 4x cos(2-3x) dx

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Q: Solve algebraically: 2x−1−arctan(√x)=0

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Q: 9 y- Arctan( 1-2x

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Q: 9 coshx - 5 sinhx 15 %3D

A: To solve  9coshx-5sinhx=15

Q: 9 y= Arctan( 1-2x

A: Use simple differentiation twice to get the answer.

Q: 6- y = (sec(2x) + tan(3x))-2

A: We have given function-  y = [sec(2x) + tan(3x) ]^-2

Q: (cos(3x+ 1))² lim 7+ 4x

A: our objective is to find the limit

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…