Find the root (7 – 7i)/2 O +7/2[cos(x/4) – isin(x/4)] O +V98[cos(r/8) – isin(x/8)] O +7/2[cos(x/8) + isin(x/8)] O + V98[cos(r/8) + isin(x/8)] +7V2[cos(r/4) + isin(x/4)] O +7V2[cos(7/8) – isin(x/8)]

Q: 1//2 x8 Evaluate: sin" (1-2x')+ cos" (2axvi-x")} dx. 2x²)+cos* 1-x4 -1/V2

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Q: In cos 2x 4. Find lim x→0 In cos 3x

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Q: 1) Verify the power reducing formula, cos-x= 0:1 holds true for x = and x= =.

A: Here I am attaching image so that you understand each and every step.

Q: 2- Exercise: Evaluate a) L{4x2 – 3 cos(2x) +5e*} b) L{4+ sin (x) – e** } -

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Q: 2) x- 2y = x°cos4x

A: Given differential equation is -   xdydx-2y=x3 cos 4xDivide throughout by x we get-dydx-2xy=x2 cos…

Q: 8 410x-32+x2 cos2x 4 Find *: (a) y =

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Q: 6. f(x) cos (4x- 16), when x = 4 (0 in the given function is in degree measure)

A: Given- fx=cos4x-16 To Find- The value of the above expression when x=4 and θ in the degree measure.

Q: V = πT -0.5x Sin 4x 4 +8x-cos2x 2 - X²-4 2²- 19.5x 1.478 -1-082

A: To determine the limit of the following equation.V=π-0.5×sin 4x4+8×-cos…

Q: 3 Find ALL solutions of cos 2x = 2 %3D

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Q: cos(3rk) In k 5k k 1

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Q: cos(x)-9=16cos(x)-1 ov

A: Here we have to solve the value of x;  8cos2x+4cosx-9=16cosx-1 over the interval [0,2π)

Q: 1) VERIFY THE POWER REDUCING FORMULA, cos"x : cos 2x+1 HOLDS TRUE FOR 2 x = - AND x =

A: To verify:   cos2x=cos2x+12, for x=π3 and x=π2   NOTE: As per our answering guidelines, we can only…

Q: Find the smallest positive solution of cos x = eX; x0 = 1 by iteration.

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Q: 1 (27 x sin nxdx 27 bE f(x)sin nxdx -sin nx -1. 1-2n cos 2nn COs nx %3D %3D The requirod f 2)

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Q: Q1: (1) Show that the value of € (-1, π), for which: sin² 0 1+ sin² 0 sin²0 1 + cos²0 cos² 0 cos²0 4…

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Q: Evaluate cos (x (x2 – 2x + 1) (2x - 2) sin (x 2 - 2x +1) (2 – 2x) sin (x? – 2x + 1) O (2x 2) cos (x-…

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Q: 1-2x²=1+x+x²³ 2²-2²-1+2+ -2(-1) (2n + 1)! x²+1 sin x- ---- cos x=(-1). - (2n)! −2+4- 6! tan 'x-…

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Q: [1] Find the Fourier series: (a) f(x) = 3 sin(2x) - 5 cos(7x) + cos(8x) (b) f(x) (c) f(x) = cos²…

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Q: 5(t - )cos3t) 3 252 + 18

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Q: Give all solutions from [2, 14]. 2 cos(x- n) = v3

A: Consider the provided question, We need to find the solution of  2cosπ3x-π=3 between the interval…

Q: π/2 0 /1-cos2xdx

A: solution:-∫0π21-cos2xdxwe know that cos2x-sin2x=cos2x1-sin2x-sin2x=cos2x1-cos2x=2sin2x

Q: (-1)"x2" Σ (2n)! 1. For all x E R, cos x = n=0 +00 (-16)"(4n+1) (2n)! c. Use the result in item 1(b)…

A: We have to prove the sum of series.

Q: π 3n The number of solutions to cos 0 - < c, with 0 < c < 1 and

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Q: Find y' (y prime) and y" (double prime)y = cos(x2)

A: To determine the expressions for the first and second derivatives of the given composite function

Q: cos 4x = cos 6y, which of the following is correct? 2x + 3y = 90⁰ 2x + 3y = 270⁰ 2x + 3y = 180⁰ 2x…

A: Given query is to find which statment is correct.

Q: C 3y° cos xydydx = O 3(1-Cos3) 5(1-cos3) cos3-1 O 5(1-Cos3)

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Q: Which of the following is a cubed root of (-/3 - 9? (A) 21°[cos(8z9) + i sin(8z9)] (B) 21[cos(7x/9)…

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Q: Let m be the number of solutions of sin (2x) + cos (2x) + cos x + 1 = 0 in 0<x< x< 1/1/2 and 7 7π n…

A: The roots of the equation: f(x)=0 are the values of x, where the graph of the function: y=f(x)…

Q: - Find all solutions for 4 cos x+V3 = 2 cos x if 0<x<2n. %3D

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Q: Find all exact solutions on  [0, 2π).   2 cos2(t) + cos(t) = 1

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Q: Find the value of k if 1 х cos(3x) dx 1 3* x sin(3x) + — сos (3x) + C. k

A: .1. ʃ (u.v)dx= u ʃv.dx - ʃ(d/dx(u) . ʃv.dx)dx       Where u and v are function of x 2. ʃ sin(ax) dx=…

Q: . (a) Write cos 3x + i sin 3x = e3ix = (cos x + i sin x)³ by Euler's formula, expand, and equate…

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Q: Express as a product a. cos 5t + cos 6t b. cos x + 2x

A: We have to express as a product  (a)  Cos 5t + Cos 6t We know that  CosC + CosD =…

Q: 3-Vx² +5 is co

A: f(x)=4-x3-x2+5,x≠2       =k, x=2

Q: For cos2(xy) = - evalu COS 4

A: Given

Q: (-1)" (2n+1)! n=0 Σ Given: sin x x² n2n+1 for x E R (-1)"(2n +1) 4" (2n + 1)! Compute the exact…

A: Given: sinx=∑n=0∞-1n2n+1!x2n+1 for x∈ℝTo compute: The sum ∑n=0∞-1n2n+14n2n+1!

Q: find a particular solution of y"-9y=-6 cos3x *

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Q: Find all solutions to cos(7t) – cos(3t) = sin(5t) on 0 <t <n 1

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Q: The set of solutions of y' = -2e-* – 12 cos(4x) + 2 is given by: а) О 2е + 3 sin(4x) + 2x + C 3 b) О…

A: Note the integration of some functions: ∫eax dx=eaxa+C ∫cos ax dx=sin axa+C ∫xn dx=xn+1n+1 +C ;…

Q: The f sin x cos²xdx is x sin 4x {A} 16 64 sin 4x x {B} 16 16 O A B O - sin³2x 48 sin³2x 48 +C + C…

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Q: Find all solutions to 2 cos(0) = v2 on the interval 0 <0 < 2ñ 0 =

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Q: 1- By using simple Iteration method, find one root of the following equation: b- e* * tan x = e-3n/2…

A: The iteration method uses the formula, xn+1=ϕ(xn) to perform the iteration.

Q: 5. Find the term representing the third har- monic for the periodic function of period 27 given by:…

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Q: 2. Solve for the fundamental periodic and sample of the equation: x(n) = 2 cos 3. %3D

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Q: 7. Algebraically solve for 0 < x < 2n a) 5-3 cos(2x) = 5+ sin(2x) а) b) 3 sin(x) = 1+ cos(2x)

A: We know, cos(2x)= 1-2sin^2(x).

Q: find y prime and y double primey=cos(x^2)

A: To apply chain rule and product rule to find the first and second derivatives of a composite…

Q: Determine the general solution of: a) -3 sin x = cos 2x b) cos 2x =1-2 cos x ||

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Q: 3 Find all solutions of cos 2x for x if 0 < x < 2n. 2

A: The solution is :

Q: 1n 1-Co1 2n

A: To evaluate ∫π4π2 sin 2x1 - cos 2x dx

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.