Let :
$x_{n} \mbox {be a sequence in R with} \ x_n \to 3, \mbox {show that } \{ x_{n}}^2 \to 9$

2. Originally Posted by flower3
Let :
$x_{n} \mbox {be a sequence in R with} \ x_n \to 3, \mbox {show that } \{ x_{n}}^2 \to 9$
I find it difficult to understand why this question is posted in an advanced forum.
I will let you work out this fact: $\left( {\exists N} \right)\left[ {n \geqslant N\, \Rightarrow \,\left| {x_n + 3} \right| < 7} \right]$.
Note that: $\left| {x_n ^2 - 9} \right| = \left| {x_n + 3} \right|\left| {x_n - 3} \right|$
It follows from that fact.