Using the result in Exercise 2.2.5, prove the following results. a) Suppose that 0 < x1 <

Question:

Using the result in Exercise 2.2.5, prove the following results.
a) Suppose that 0 < x1 < 1 and xn+1 = 1 - √1 - xn for n ∊ N. If xn → x as n → ∞, then x = 0 or 1.
b) Suppose that x1 > 3 and xn+1 = 2 + √xn - 2 for n ∊ N. If xn → x as n → ∞, then x = 3.
(c) Suppose that x1 > 0 and xn+1 = √2 + xn for n ∊ N. If xn → x as n → ∞, then x = 2. What happens if x1 > -2?