16. Find the solution of the equation [cos(x) +1][sin(x) +3] = 0 in the interval [0, 27). 37 i) 5 i) 7 iii) 27 iv) 7 v) not listed

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Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about

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A: Given that w=cos(x+y)+sin(x-y) Now, ∂w∂x  = First order partial derivative of w with respect to x…

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Q: 12. cos-1 %3D A. 7n O B. 3 6 C.

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Q: a) m - 1 b) m – 2 Q.8) The characteristic equation for y"" + 3y" – 4y = 0 , is : b) 2' = 32?-4 c) m…

A: To find out the characteristic equation.

Q: 10. Find the solution of the equation [tan(x)+v3][cos(x)+7] = 0 in the interval [0, 7). 27 57 iii)…

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Q: QuestionTO cos( z+ Da sin(e-2+ In(z)) + C 4 Ob. -4 sin(e-z+ In(z)) + C Oc. --- sin(e-z+ In(z)) + C 4…

A: Given query is to evaluate the integral.

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: O y(1) = c, e*" + C,e For each set of solutions below, match the solutions to the general s Prompts…

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Q: Consider the equation 4y" + by' + cy = 0 the constants b,c,m,n are real and different from zero, the…

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Q: Consider the following difference equation: fk k = 0, 1, 2, · . . 1+ fk' fk+1 = with fo is…

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Q: 7) Consider yu- 3y' -2y= 3t cos(t) a) Find the complementery solution, 6) Fnd the par ticuler yo e…

A: Given differential equation is  y''-3y'-2y=3tcost we have to solve this.

Q: 33. If 2 = [i(cos0 + isin0)]" then arg(2) A -2n0 + n B n0 + n C 2n0 rev D 2n0 – n

A: Given complex number is z=icosθ+isinθn.

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: (25) Let k and n be positive integers. Prove each of the following: sin (n2) dz = | cos (nx) dz = 7.…

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Q: How many distinct solutions does the equation sin(3x) = have on the interval [0,27)? 2 (A) 1 (B) 3…

A: Sine angle is positive in first and second quadrant only. Also,  To solve any trigonometric…

Q: Q7: Í sin(3z)cos(4z) dz = a)cos z- cos(72) + C b) -tcus x -os(Ix) + C %3D Qe S sin'x cas d = 2).

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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: o find for: y = sin(x") + 2* +n

A: Given,          y=sinxx+2x+π

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A: Answer 2 only.

Q: 8. In right triangle XYZ, cos X = and cos Z =. If XY = 32 then what is the length of XZ? 15 17 17…

A: Given, Right triangle XYZ. cosX= 8/17 cosZ= 15/17 XY= 32

Q: 12) f)=sin(x) 0<x<1 Ans. 24 1 (₁ A 7 (1)(3) 1 -cos(2x) +- -cos(4x) (3)(5)

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Q: -1 L-1 [wcose+ssine` s²+w² a. sin (wt + 0) b. sin (t + 0) c. cos (wt + 0) d. cos (t + 0) 2}, w & 0…

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Q: 1. By considering (1+ expi®)", prove that "C, cos r0 = 2" cos"(0/2) cos(n /2) (ii) ►"C, sin r® = 2"…

A: First, expand the given complex function: