Chapter 5, Problem 28SE

(Requires calculus)Suppose that the sequence $x_1,x_2,\mathrm{...}{x}_n,\mathrm{...}$is recursively defined by $x_1=0$and $x_{n+1}=\sqrt{x_n+6}$.

Use mathematical induction to show that $x_1<x_2<\mathrm{...}<x_n<\mathrm{...},$that is. the sequence $\left\{x_n\right\}$

1. is monotonically increasing.

Use mathematical induction to prove that $x_n<3$forn=1,2,....Show that lim $x_{n\to \infty }{x}_n=3$.