Consider the following ODE y" = 4y What is a possible solution (select all) Select one or more: O a. e2 b. e-2r O C. e" O b. d. 73e2" O e. sin(x) O f. cos (2x) O g.a O h. -2e -2x

Q: If S (x) = - sin(x), then f (11) (x) is equal to – sin(x) B B -cos(x) CosX sin (x) D O cos(x) A,

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Q: Consider the following. g(x) = V3 cos(2x) + sin(2x) (a) Express the function in terms of sine only.…

A: We know that the following trigonometric identities . sin ( a + b) = sin a cos b + cos a sin b  And…

Q: If f (x) = – sin(x), then f (10) (x) is equal to A - sin(x) В - cos(x) C sin(x) D cos(x)

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Q: Solve for the approx- two decimal places. 2 cos (0) + 2 cos(E

A: Given trigonometric equation is: 2 cos2 θ+2 cos θ-1=0 Solving we get, cos θ=-2±22-42-122⇒cos…

Q: 3TT Find sin (sin 0), if n<0< 2 -1 Select one: O e+ t O e-T

A: To find: sin-1(sinθ),   if π&lt;θ&lt;3π2

Q: Evaluate the following integral. 1/6 | (sec x – cos x) dx 1/6 - 2/31+ 11 8/3 (sec x- cos x) dx =…

A: Given that: ∫0π/6(sec x-cosx)2dx

Q: 9) 5olve For OLO<2M Cose+sin A =1 2.

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Q: Evaluate the following integral. 3 4 4 cos '3x xp. sin 3x 1 18 4 4 cos '3x dx = V1- sin 3x 18 (Type…

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Q: 3. S cos ædæ from a = 0 to b = 5

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Q: Evaluate | e'(sin(1) + e*)°dt using an appropriate substitution.

A: Given : ∫etsin1+et9dt

Q: Using an appropriate substitution, f sin³ (x)cos®(x)dx is equal to: sinx + C sin13x + C 13 sin11x…

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Q: Evaluate: S2-* tanh21- dx 4. A. –In2 In | cos h21- |+C C. In | sec h21-x | +C In 2 B. -4ln | sech?…

A: We are authorised to solve only one question, please repost remaining questions. Indefinite…

Q: 3 Find 16(3 sin(x)) cos(x)dx if | Ax)dx = 16 O a.-256/3 O b.-128/3 Ос. 128/3 O d. 256/3 O e. No…

A: 7. The integral is given by I = ∫0π216f3sinxcosxdx                                       ........(1)…

Q: Evaluate D3(sinx – 4e) A cos x-32 ex B -cos x-32 e?x -sin x-32 ex sin x-32 e2x

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Q: 1. Determine the value of cos(2x+2y) if sin z 3 and tan y = - for 4 sysa. for 0sxs: VI VI

A: Given : sin x = 3/5 and tan y = -3/4

Q: DIFFERENTIATE THE GIVEN y = x² co sec™ 3 -1 * COS

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Q: Calculate L4 for f(x) = 84 cos ()

A: Given,           f(x)=84cosx2  over 2π4, 2π2

Q: If f(x) = sin(cos(2x)), then find f' O-1 O -2 O 1 ||

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Q: sin x sin ydx+ cos x cos ydy = 0

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Q: Evaluate: e* cos (7e*)cos (4e*) dx (A sin (3e*) +sin (11e") +c - sin (11e*)+C - sin 6. 22 ® -cos…

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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: Please find all 0 <o< 2m, for which .. (a) tan (을) =D v3 (b) 3 sin²(0) + 4 = 5 (c) 2 cos(ln(x² + e")…

A: As question has many subpart we are giving solution for first three subpart. If you want solution of…

Q: ly sinfcot(cos x), then y (2) is Select oner A 2. • Co CO O DR ENone of these

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Q: Which option equalsS x sec2x dx ? Exactly one option must be correct x secx tanx - In(cosx) + C O x…

A: Hence option (b) is correct.

Q: 4. Evaluate the following in terms of Gamma function sin (4r) cos (2r)dr

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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: Evaluate x2 dx Select one: on O(sin (2r- 1) + 2(2 (2ain (r) + sin(2si To (stn(2 1I) 2(2r sin(2sin

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Q: 2. Find g'(x) for g(x) = x cos-l-V1- r²+ez³ cos z. [Simplify answer as much as possible.]

A: topic -derivative

Q: 47. Show that y = sin(tan-x+ C) is the general solution of y' = /1 – y²/(1+x²). Then use the…

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Q: One of the correct steps to evaluate A B) None Ⓒ [+ + [ 1².40-16.4040] -S de cos 40d0 + [ 140 + 1 =…

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Q: Which of the following is equal to f(x)dx where S(x) =- sin(x) if 0<x< a/2 l cos(x) if 1/2<x<a } -2

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Q: Consider (D² + 1)y= se = sec x . If y, = f cos x + g sin x, what is f and g ? A = In cos x|, g = x f…

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Q: The suitable substitution to evaluate sin 4(x+2) dx is None OA [1-cos8(v+2)] В. [1+ C. 2 + cos8(r…

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Q: 3. Show f cos2n Ode 277 sin-n Ꮎ ᏧᎾ = 27 22n 11.1 n = 1, 2, 3,...

A: Using Cauchy integral formula.

Q: Q3. Calculate L{e-ª cos(2t – 1)} COS

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Q: 4. Prove that the identity is true. 1- cost e = sin² 0 1+ cos e

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Q: 4) Differentiate each of the following: a) y = - cos²x c) f(0) = sin(20 — π) b) y = sin(20) - 2…

A: Differentiate the following  a) y=-cos2x b) y=sin2θ-2cos2θ c) fθ=-π2sin2θ-π

Q: Evaluate sin (4x + 14) dx cos (4x + 14) Ocos (4x + 14) + C O-cos (4 + 14) + C -cos (4x + 14) +C…

A: Integration

Q: Evaluate: a sec a tanxx dx from a = 0 and b = O 12- 1/ 0용 + 1 O none of these O v2+ 1

A: Given query is to eveluate the integral.

Q: The cos³4 dy is {A}-sin+sin³¹+C 3 4y 4 3 3 {B}sin-sin³¹+ C 3 4 3 (c)-sin-sin³+C {D}sin+sin³+ C

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Q: Find cos (0 + p) given that cos 0 = 2 and cos p = 2 and that 0 and p are between 0 and t/2.

A: For the given values of  Cos(θ)=1213 Cos (ϕ) = 35 Cos(θ+ϕ ) is evaluated as shown below

Q: х If f(x) = cos(1? + 1) dt, then find f'(x). %3D Select one: O A. None of the others O B. sin(x + 1)…

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Q: Evaluate D°(cos x +e-2") A cos x – 32e-2x (B) sin x + 64e -2x (c) - sin x – 32e -2r (D - cos x +64e…

A: Here we have to evaluate      D6(cosx+e-2x)

Q: Using an appropriate substitution, S sin° (x)cos (x)dx is equal to: cos13x cos11x +C 11 cos1x cos°x…

A: To evaluate the given integral

Q: Evaluate D6(cosx+e-2*) (A sin x +64e -2 B cos x – 32e-2r (c - sin x – 32e-2x cos x + 64e -2x |

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Q: 4 Find 20(4 sin(x)) cos(x)dx if Ax)dx = 16 %3D O a.-160/3 O b. No correct answer O C. -80 Od. 160/3…

A: Consider: ∫04fx dx=16. Evaluate: ∫0π220f4sin xcos xdx. Let 4sin x=t. Differentiate. 4cos x dx=dtcos…

Q: 5. Evaluate SO-2²πT ydx = 3π₁ given x = 0 - sine, y = 1- cos -0

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Q: Find :L [cos h 5t sin 2t] a.) (s²-25)(s²+ 4) [ल. 2s b.) (5-5)²+4 c.) 1. (5-5)²+4 (s+ 5)?+4 dl.)…

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Q: А. Find the general solution of the following first-order ODE ху' — у + 2х3 sin? (2)

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