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Thread: Proving the limit of a function

  1. #1
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    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 $\displaystyle |f(x) - L| < \epsilon$ but the question is use the (N, ε) method prove $\displaystyle lim_{x \rightarrow \infty} \frac{7n + 3}{8n + 5} = \frac{7}{8}$

    I've read though the notes ive taken on this but still dont get it id be really grateful for some pointers
    Last edited by renlok; May 17th 2010 at 03:28 PM.
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  2. #2
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    You have to show that for any $\displaystyle \epsilon > 0$, there exists an $\displaystyle N$ (depending on $\displaystyle \epsilon$ ) such that whenever $\displaystyle n > N$ we have that $\displaystyle \Biggl| \frac{7n + 3}{8n + 5} - \frac{7}{8}\Biggr|<\epsilon$.

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