10. Find the solution of the equation [tan(x)+v3][cos(x)+7] = 0 in the interval [0, 7). 27 57 iii) iv) v) not listed i iv O v

Q: 5. Solve tan² (2x) = 1 in the interval [0, 2π).

A:

Q: b) 6(sin x)² + cos 2x + 1 = 0 [0,2π] I

A: Solution6 sin2x+cos 2x+1=0we know cos 2 x= 1-2 sin2xput this value in the given equation,6 sin2 x+…

Q: 7. f cos xdx

A: The given integral is Cos4x

Q: find the valups of 'a'and b' that nakes 8x2+ 8 x2+ +5 X L-1 K(x)== 6 x= -1 con tinuous at x =-| x 7-…

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Q: Prove using the IVT cosx = cos-1x has a solution in (0, 1).

A: cos x = x   rearrange to x - cos x = 0

Q: (3Vr + 2e) dx.

A:

Q: Derive formula (2) on page 601. cosucos v 5lcos (u – v) + cos (u + v)]

A: Given equation is cosucosv=12cosu-v+cosu+v. cosu-v=cosucosv+sinusinvcosu+v=cosucosv-sinusinv

Q: Which function has the same graph as y= 4 cos y = 4 sin x+7 ) y = 4 sin 3 y = 4 sin X- y = 4 sin

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Q: c) y = (x-2) 3 x² (x-1)(x+5)4 [Hint: use logarithmic differentiation]

A:

Q: 11. Find the solution of the equation [2√3 tan(r)+2][cos(z)-5] = 0 in the interval [, 2). E 3 iii)…

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Q: 3) v = C,e2x cos 3x + Ce sin 3x 2x

A:

Q: 2. S tane sec4 0 d0

A:

Q: 6. On [0, 27) solve equation 2 cos x cos 2x - 2 sin x sin 2x = 1

A:

Q: ) Prove that tanh'x = tn/itx, X€ (-1,1) i) , Sinh 'x and tanh'x Find the derivative of coch'x

A: (1). We have to prove that:   tanh-1x=12ln1+x1-x

Q: Solve Q11

A: 11. Given that the series                      x∑m=1∞mamxm-1+∑m=0∞amxm

Q: a) 12 Q.7) To write the power series £=3 4m as the form -4m a) m - 1 we must shift m to become : d)…

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Q: . Let z = 1+ cos 0 + i sin 0, where - < 0 <0. (a) Show that |z| = 2 cos -1 and arg z = (b) Hence…

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Q: z.e +4 a'z cos(2x+y) z.e Solve ax 4 əx-əy axəy

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Q: the sum of sin h 2x and cos h 2x

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Q: х. у 2) w=¨+2,x= cos“(t), y = sin°(1), z =-, at t = 3 Z Z t

A:

Q: 18. Solve 2 tan r-1 0 over [0, 27).

A: Unlike the sine and cosine functions, the tangent function is π periodic. That is, if the point (x,…

Q: Q.12) The solution of y" + y' = 0 by using power series method , is! %3! a) y(x) = a, – a,(1-+ b)…

A:

Q: Solve

A:

Q: Sæ³ cos(x*) dæ =

A: We solve it by u part method , ∫x3cosx4dx Let u = x4 Differentiate both side , we get   du = 4x3dx…

Q: 1 – - 1 + z" If z = tan show that cos a =

A: Given: z=tan α2To prove that cos α=1-z21+z2

Q: Find LT of (i) e(2 cos 5t – 3 sin 5t) 3t (ii) e²ª cos? t (iii) e* sin 2t cos t

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Q: 13. Differentiate 1 3 y = 2x2 + 6x3 – 2x2 а. 2 6 b. у 3 —t 4 3 x2 3 x4 x2 'x3 y = sin³ [cos(tan(3x –…

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Q: 2x 2)/3x* 2) [3x* - 9x² +1 V9-x² dx .2 3) [ sin xcosx dx x cos.x 4) S sin² xcos 4) sin x cos x dx

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Q: 8) S dx it sinx + cos x a) in (1 + tan =) + c b) In (i - tan £) + c c) - In (1 + tan x) + o 2 d.)…

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Q: Sz sin2m-10 cos2n-10 —— В (т, п) 2

A: It is known that, βm,n=∫01xm-11-xn-1dx

Q: c) y(x) = c, + cz + Acos3x + Bsin3x Q.6) The singular point (s) of (x² + 4)y" – x y' + 4y = 0 , is…

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Q: Madaurin f(x) = cos(7)

A: Find the Maclaurin expansion of  f(t)= cost

Q: 1) S“(cosx)" dx. 2) Г(-4). 3) В (10,9) 4) Sº x° e-2* dx Ja-x)i 5) o

A:

Q: Q2) A Differentiate the following ( 1)y= [(5x) (4- 2x)]²

A: As per bartleby guidelines we only give first question answers.

Q: 1. If Z = sin r+ 2 I+1 6. - ", find dZ/dr.

A: differentiate with respect to x

Q: Prove that sin? 0 – sin* 0 = cos? 0 – cos* 0. cos“ 0.

A: We can use the trigonometric identity, sin2θ+cos2θ=1 sin2θ=1-cos2θ.

Q: 1) Solve det [i4(îĥ.ở)] where ở li ). and în = COS + sin j. (i = V-1)

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Q: Find Lt+1)²-e' sin² t + cos(t+1 ++ π)}.

A: Given :

Q: a) 2(sin x)² - 1 = 0 [0,2π]

A: a) 2(sin⁡x)2−1=0[0,2π]

Q: -1 -1 18. Show that cos (-x) =T- cos x

A: We have to prove that cos-1(-x) = π - cos-1x

Q: 3) Solve S(4cos? x+4 sin? x)dx

A: Given:

Q: Q.1) The general solution of the equation y e' cosA a) y(t) =c, +c; x +c,¢ ' de' cosa Re' sinx b) y…

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Q: 1) y = cos (48 + 11)+1 1 2 6

A: