Let x₁ = √2, and x1 Xn+1 = 2 + √√xn, n = 1, 2, 3, .... Prove that the sequence {n} converges, and find its limit. Prove by induction. 1 Prove that the sequence {n} is monotonically in creasing and is bounded above.

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Q: 5. Find the Fourier Series of the following functions: (a) f(x)= -1,-1<x<0, 2, 0<x<1, f(x+2) = f(x).

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Q: Solve the system +8 +t 4x1 -5x2 -I1 +2₂ +4x3 +2x4 +2x3 +2x4 = 3x₁4x₂ +6x3 +4x4 = -2x1 0550 +2x₂ +4x3…

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Q: Solve the following the exact differential equation : (3x^2y-6x)dx+(x^3+2y)dy=

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