# Math Help - Proving the limit of a function

1. ## Proving the limit of a function

I can't get my head around these types of questions i know how to prove a limit you use $|f(x) - L| < \epsilon$ but the question is use the (N, ε) method prove $lim_{x \rightarrow \infty} \frac{7n + 3}{8n + 5} = \frac{7}{8}$

I've read though the notes ive taken on this but still dont get it id be really grateful for some pointers

2. You have to show that for any $\epsilon > 0$, there exists an $N$ (depending on $\epsilon$ ) such that whenever $n > N$ we have that $\Biggl| \frac{7n + 3}{8n + 5} - \frac{7}{8}\Biggr|<\epsilon$.

First put $\frac{7n + 3}{8n + 5} - \frac{7}{8}$ over a common denominator and simplify. You should then be able to get $N$ from the result.