# Prove using the precise definition of the limit

1. Mar 17, 2014

### TheRedDevil18

1. The problem statement, all variables and given/known data

lim x→2 (x2+1) = 5

2. Relevant equations

0 < |x-a| < delta

|f(x) - L| < ε

3. The attempt at a solution

0 < |x-2| < delta

|x2-4| < ε

|(x-2) (x+2)| < ε

|x-2| |x+2| < ε..................and I am stuck here, any help

2. Mar 17, 2014

### LCKurtz

Continuing your analysis:$$|x-2|<\frac \epsilon {|x+2|}$$You are trying to get the right side small by getting $x$ close to $2$. So you don't want the denominator to get close to $0$. Can you keep it away from $0$ if $x$ is close to $2$? That's the idea you need to pursue.