sin(e)de 4+cos (e) In(4+cos'(e)) +c -sinh -sinh cos (0) sinh (cos (0)) +c 2/4+cos (0)

Q: /1+cos x + V1- cos x X =-+÷,0<x<“ 4 2 V1+ cos x - V1-cos x - cOs X

A: Using trigonometry formulas we solve here given question

Q: * (D'+1)y(x) = tan(x) 1-sin(x) 1+sin(x) 1+cos(x) - y,(x) = sin(x)In m(x)s03 = (x) 2- -- y,(x) =…

A:

Q: cos (x sin )=√₁ (x)+2 J₂ (x) cos 26+2 J₁ (x) cos 44+... sin (x sin )=2 J₁ (x) sin +2 J, (x) sin 36 3…

A: Using generating function of Bessel functions

Q: cos x-2 cos 3x + cos 5x b. cos x +2 cos 3x + cos 5x :-tan x. %3D

A:

Q: y=-sec^-2 (In x)

A:

Q: Given y = 4 cos(x) - x. Determine where the function is increasing in [-2, 7]

A: Given y = 4 cos(x) - x

Q: cos.2x 25. cos.x - sinx A sinx 3-.cos x + sinx C 2:cosx + sinx A - cos.x :D D cosx -2-sinx

A:

Q: sin 3x 22. Integrate: JS dx V25-cos² 3x A. -sin-1 (os*) + C 'cos3x' (cos 3x` C. -sin *) + C 15 B.…

A:

Q: sin 2 dx 4 Inx |(xy)sin*(! e ]dy + ху tan

A:

Q: sin 5x + sin 3x 2 cOS X 4 sin x cos 4 sin x cos x 3 X COS -

A:

Q: sin (3x) + cos (3x) cos(x) – =1+4sin(x)cos(x)

A: We use sin(3x)= 3sinx-4sin3x and cos (3x)= 4cos3x-3cosx .

Q: Cos (x-y) t cos (Xty). COS 2cos x COSY

A: (Cos(x-y) + cos(x+y)) /2.cosx.cosy =?  We know that cos(x-y) = cosx.cosy+sinx.siny…

Q: (i) Express sinx – V3 cos x in the form A sin(x – a) with A > 0 and 0< a < - (ii) Find the general…

A: i) Given that expression is sinx-3cosx.It is required to write the given expression in the form…

Q: sin 2x 4. tan x = %3D 1+cos 2x 19 5. tan %3D = CSC X - cot x

A:

Q: 20. cos x 3 cos x -V2 cos x csc x; xe[0,2n]

A:

Q: sin x cos x – tan x cos² x dx cos x cos? x sin x dx cos3 x 16. = sec x dx + cos x Let u = cos x ; du…

A: It is given that    ∫cosx-tanxcos2x dx We have to evaluate it.

Q: tan6(x) cos4(x) sin²(x)sec³(x) [7sin²(x) + 9cos²(x)] + C A 63 tan²(x) [7tan²(x) +9] + C B 36 Ⓒ…

A:

Q: cos 2x – cos x lim | x→0 sin x O -1/4 О 3/2 O -1/2 O -2/3

A:

Q: Prove that

A: Given:d2ndx2nsinx=-1n sinxd2ndx2ncosx=-1n cosx

Q: sin(5x) dx 2+сos(5x) اخترأحد الخيارات х + tan(5x) + с.ао —In | 2 + сos(5ӕ) | +с.Ь 1 +c.c 2+сos(5ӕ)…

A: Since , in the given integration problem we have derivative of denominator in numerator so we will…

Q: - sin sin -y = sin (x+y) Prove that cos Xcos 4 -y 4 -x sin 4 X - 4

A:

Q: cos cos 30 - cos 50 lim- 0>0 s 70 - cos 90 cos

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Q: (cos y+ y.cosx-ec*.sin x)dx+(sin x – xsin y)dy =0 cos.x

A:

Q: S tan -) dx = a) x tan-1 (-) +÷In(x² + 1) + C b) x tan-1 () +글x2-글In(x2 + 1) + C c) x tan-1 (는) +글x2…

A:

Q: 2 (sin x cos x + x) + C - 2 (sin x cos x + x) + C (sin x cos x + x) + C -(sin x cos x + x) + C [(cos…

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Q: V1+ cos x + v1- cos x X =-+-,0<x<. 4 2 an 1+ cos x - V1- cos x - cOS X VI

A:

Q: 6. h(x) = 5x sin-1x 7. h(x) = tan x – tan-i x 8. h(x) = 3 sec-x 9. h(x) = 14 cot"x+ 12 cos-x 10.…

A: Since you have posted multiple questions we solve first question for you  To get the solution of…

Q: 2+ cos (1 + x»'½) .0.5x dx 22 cos (1+x³/2) V1+0.5 sin x 2,0.5x dx|

A: By using Simpson/Trapoizodal rule.

Q: *y=(sin(x)+cos(x))cos(x). dyldx -sin 2(x)+cos*2(x)+2cos(x) -sin 2(x)+cos 2(x)-sin(2x) O

A:

Q: cos*(x)dx

A: According to integration reduction formula ∫cosn(x) dx=n-1n∫cosn-2(x) dx+cosn-1(x) sin (x)n . For…

Q: integral e -x cos 2x dx

A:

Q: ✓cos x lim x 0 1 cos x - -

A: The given limit is limx→01-cosx1-cosx

Q: 6 x° cos(x) dx =. 6 x³ sin(x) + 18 x² cos(x) – 36 x sin(x) + 36 6 x³ sin(x) – 18 x² cos(x) – 36 x…

A: Integration by parts  ∫udv=uv-∫v.du

Q: cos(x (*). cos(x + h) – cos x cos h – 1 sin h - - sin x · h COS x h h

A: Require to verify the identity cosx+h-cosxh=cosxcosh-1h-sinxsinhh

Q: sin- In?| 4+ tan-'cos- dx 2 COs- 1+ cos 4+ tan-'cos In2 4+ tan-'cos- dx 2 2sin- 2 (A) 4+ tan-'cos- 2…

A:

Q: Maclaurine’s series of ∫((cos^2(x) dx)

A: To find → Maclaurine's series of ∫ cos2 x dxSolution →                       ∫ cos2x dx = ∫ 1+cos…

Q: sin^2 x + sin x cos x over cos x − 2 cos^3 x

A: This question is based on Trigonometric Formulas to simplify question.

Q: sin x – cos r cos z cos 2x sin x + cos x 1+ sin 2x

A: Given, sinx-cosxsinx+cosx We need to prove that the value of sinx-cosxsinx+cosx is -cos2x1+sin2x…

Q: y. x -. cos(- + cos(- 2 4 х — у, 2 sin(- 4 = cos x - sin y 2

A: Here, the objective is to prove the following: 2sinπ4+x-y2cosπ4+x-y2=cosx-siny

Q: Q-2. Form the first-order differential equation of e =sinx Q-3. If f'(x) f(x) and f(1) =1 then find…

A:

Q: / Vtan(x) d.x sin(2r) I Vtan(x) -dx sin(2x) -d.x sin x cos x /cos x 2 Multiply by something that is…

A: We have to find integration

Q: 4 sin x cos x + 2 sin x - 2 cos x - 1 = 0

A: first factorize the given equation and than split two product equation  detailed solution is given…

Q: lim cos (x) - Cos (y) 3. cos cy} Sin (e) - sinly'. பி Sin(x)

A:

Q: cos 2x - cos2a Integrate cos x-cosa

A:

Q: (1+siny)[1+sin(-y)]=cos2y

A: Given:

Q: cos 3tdt 17. S- 1 sin 3t |sin² 3t-- 4

A: Topic = Integration

Q: 5.) cos (x -) + sin ( – x) = cos x cos (x -) + sin ( - x) = 3

A: Since multiple questions are asked, according to guidelines answering first question. Cos60 =1/2…

Q: cos (x)+cos(x+x)= 0 = cosʻ (x)+cos(T+x)=0

A: cos2(x)+cos(π+x)=0 use trigonometric identity cos(π+x)=-cos(x) The equation becomes…

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.