sin( 2 cos (x/ 20 )) = Select one: O 2x (400 - x )°/(400 - 2x) O 40 x/ (400 + x) O ( 2x - 400 ) / 400 (400 - 2x)/ 400 O 40 x/(400 - x") O 2x (400 - x )/(2x- 400) O 2x (400 - x)*/400

Q: cOs x tan x 28) lim sin 3x 29) lim x→0 2x x3 + 2x2 + x 30) lim x→-1 x4 + x3 + 2x + 2 x3 – 2x2 + 4x –…

A:

Q: [In(x²)-ex cos(x-1).tan(Tx) 20. lim 2x2-x sin2(1-x) X-1

A:

Q: 2 cos(4x) – 4x? – 2 - - 8. lim x→0 sin(2x) – x2 – 2x -

A: Topic = Limits

Q: 1 -sin(2x)% = (D²-1 -1 sin(2x) 125 O ibs

A:

Q: O yotan' (x'+3x-s)+ sin (x²s 2x -1)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Evaluate cos x+ 2 cos x+1 dx sin x sin x - 3 cos x cost x 7. +x+c 2 cos x +x+c 3 cos X- cos x (sin x…

A:

Q: |5sin(4x + 5) sin(2x --) dx

A: We need to evaluate the given integral. We will use the formula  Cos(A+B)-Cos(A-B)=-2 SinA SinB

Q: 1 - cos 4x 1 + cos x dx

A: The given integral,     ∫1-cos4x1+cosxdx

Q: cos 2x–1 lim COS х— 1 cos x-1

A: limx→0cos 2x-1cosx-1

Q: 3) f(x) = ln(x5 - cos²x) 5) f(x) = xsinx 4) f(x) = x² 1 + x³ 1 6) f(x) = x¹ tan- X

A:

Q: 1-cos 3x +C dx 1+ cos 3x 3sin 3x

A:

Q: 2 cos(8x) – 8 x² – 2 lim - sin(3x) — 2? — За

A: Here we apply l Hopital's rule.

Q: find dydx 15. y = (sec x + tan x)(sec x - tan x)16. y = x^2 cos x - 2x sin x - 2 cos x17. ƒ(x) = x^3…

A: To Determine: find the derivative  Given: we have y=secx+tanxsecx-tanx Explanation: we have…

Q: Integrate sin 4x cos 5x + cos 4x sin 5x

A: SinAcosB+cosAsinB=sin(A+B)

Q: 2-sec2x: COS2X = COS X

A: Given query is to verify the identity

Q: limx→0 (1−cos(5x))/(1−cos(9x))

A: Used L'Hospital rule

Q: Compute : , log,(cosx) d dx - sin x A. (In 2). cos x 1 B. (In2).cosx -(In 2). sin x C. COS X -In2 D.…

A:

Q: sin(4x) cos(2x) dx = cos (2x) cos (6x)' sin (2x) cos (2x) сов (10х) 4. (2x) sin (10x)+ c sin +c 10…

A: Use formula 2sinAcosB=sin(A+B)+sin(A-B)

Q: 7x cos()-7x [sin(-2x)sin(5x)sin(7x)] – lim 2x cos(x) lim x-0 5x?

A:

Q: Evaluate sin 2x sin 4.xdx 2 b. sin 3 2x + C 3 1 a. sin ' 2x+C 3 c. cos' 2x+C 1 с. 3 d. -cos 2x +С 2

A: To evaluate the given integral: ∫sin 2x sin 4x dx

Q: 3 (4+sin-15x)° dx (8) V1-25x2

A:

Q: 3 cos(x) sin(4x) 3. lim x→0 2x

A: Solution:

Q: FIN 2 dx

A: Note:- In given problem, according to written way sin2x is multiplied by 3x+1. If you want solution…

Q: 1-cos 3x +C 3sin 3x dx 2. 1+ cos 3x

A: We have to prove given integral.

Q: 3. sin(3x) = 3s in x – 4sin³ x

A:

Q: 12. etan 2x sec² 2x dx 13. Jdx/(x²-4) 14. (2x¹-x²) dx / (2x² + 1) 15. f (sec²x) dx/(√(1-4 tan² x))…

A: Given

Q: 1) y = x3 + sin x² + sin-1 5x 2) y = 32x + In (sin x²) + In(sin¯' 5x)

A: some functions are given , we have to find its derivative

Q: 2. 2. COS X Sinx lim 4x-X

A:

Q: 2 cos (x2) - 4x 2 sin (x2)

A: 2 cos (x2) - 4x 2 sin (x2)

Q: Suppose: sin(x) = -0.1 cos(y) = 0.5 tan(z) = -4.3 Then, sin(-r) =| 0.1 cos(-y) = 0.5 tan(-2) = 4.3…

A:

Q: lim (x approaches 0) of [sin(5x)cos(6x)]/(x)

A:

Q: - 3in 2 X sin X- COSX

A:

Q: 8. 5 cos²x - 3tan x COS X dx

A:

Q: Find sin 2x, cos 2x, and tan2.x if sinx= -- 3 and x terminates in quadrant IV. V13 sin 2x cos 2x tan…

A:

Q: (3 tanx-2 cos y)sec" xdx + tanxsin yay = 0

A:

Q: x*sin (2x) dx a. ** cos(2x) – x³ sin(2x) –r² co. 3 x² cos(2x) +x sin(2x) +- cos(2x) + C 4 1 cos(2x)…

A:

Q: 1. Integral of x sin^3 (x^2) 2. Integral of sin^4 3x

A:

Q: Solve using an integral cos²(x) + 2cos²( cos³(x) .dx

A: Evaluation of the integral

Q: 1) f(x) = x5-x¹ + x² - x +² 2) f(x) = sin³x - e³x² + ln(1 + 5x²) 3) f(x)=√1-x² sin-¹ x 4) f(x)=√√x +…

A:

Q: x where 3π/2 ≤ x ≤ 2π. 1 + sec²x = 2 + cos²x + sin²x

A: Here we use formula of trigonometric equation.

Q: 1- cos 4x sec2 2x – 1 = 1+ cos 4x

A: Question is solved.

Q: cos x sin x dx 4. sin 2x cos 2x dx 5. cos x sin* x dx 6. sin 3x dx 7. sin³ x cos? x dx 8. 3.

A:

Q: 1. f(x) = cos 3x2. y = - tan 12x3. f(x) = sec x? 4. y = sin(2x² + 5)5. y = 12 csc6. f(x) = sin(x +…

A:

Q: 1)f(x)=sin³ 2x 2)f(x) = 4coshr 3)f(x) )= sinx cos*x 4)f(x) = e*cosx 5)f(x) = 8 Inx %3D

A: image is attached

Q: Solve cos 2x + cos x = 0 for x if 0 < x < 2n

A:

Q: B. - sin3 p cos 3p sin 3p cos 6p – sin 6p cos 6p H. sin 6p - cos 9p - sin 9p K cos 9p sin 9p LL

A:

Q: 1+ cosx + sinx sinx 1+cos x 2sec x 2csc x 2csc 2x 2sec 2x X.

A:

Q: 5) 3tan-1x + sin-1x = 4

A:

Q: sin- In2| 4+ tan¬'cos- dx 2 2 1+ cos- |4+ tan-'cos= 2 2sin- In2| 4+ tan-'cos- |dx 2 2 A 1+ cos2…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.