answer ALL the questions CORRECTLY. please show complete solutions. Thanks

(3) Suppose that Xo 2 2 and X, = 2+ VX-1 - 2 for n E N. Use the Monotone Convergence Theorem to show that either Xn - 2 or X, - 3 as n - co. (4 points)(4) (7 points) Suppose xo = 2V/3, yo = 3, sh 2xn-lyn-1 Xn= and yn = VXn yn-1 for all n E N. Xn-1 + yn-1 Prove that (a) xn I x and y, T y as n - co for some x, y E R ; roduce (b) x = y and 3.14155 ) Note: If (X,) is monotonically decreasing (resp. montonically increasing) and converges to x then we write x, I x (resp. Xn T x). Thus, proving this requires the use of the Monotone Convergence Theorem