**Apply the limit definition to prove [tex]lim_{n\rightarrow\infty}\frac{n^{2}-1}{2n^{2}+3}=\frac{1}{2}[/tex]**

**(question stated above)**

**I started by writing it as |f(n) - 1/2| and attempted to reduce it, but I don't think it's reducible so I am not able to simplify it..**

By looking at it further, it stuck me because I don't know where to go with this exactly. I know I am supposed to come up with this arbitrary [tex]\epsilon[/tex] then somehow prove that |f(n) - 1/2| < [tex]\epsilon[/tex]. I need to know what are the exact steps to prove stuff like this...

By looking at it further, it stuck me because I don't know where to go with this exactly. I know I am supposed to come up with this arbitrary [tex]\epsilon[/tex] then somehow prove that |f(n) - 1/2| < [tex]\epsilon[/tex]. I need to know what are the exact steps to prove stuff like this...