How to prove a limit exists using the epsilon delta definition of a limit - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-21T19:17:11Z http://mathoverflow.net/feeds/question/75804 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/75804/how-to-prove-a-limit-exists-using-the-epsilon-delta-definition-of-a-limit How to prove a limit exists using the epsilon delta definition of a limit Free 2011-09-19T01:08:21Z 2011-09-19T02:14:47Z <p>I understand how to find a limit. I understand the concept of the epsilon delta definition of a limit. Can you walk me through what we're doing in this worked example? It is from my student solutions manual to my textbook. I need help understanding what we're saying here, and why. I understand the math expressions, but I do not understand why we chose the ones we did, and why and how they prove anything. Can you help?</p> <p>Find the Lim as x --> 1 of (x+4) and prove it exists using the e-d def of limit where e = epsilon not the famous constant, and d = delta... By direct substitution, lim is 5. Understood. Now, here's where I start to get confused...</p> <p>Let e > 0 be given. </p> <p>Choose d = e.</p> <p>0 &lt; | x-1 | &lt; d = e</p> <p>| (x+4) - 5 | &lt; e</p> <p>| f(x) - L | &lt; e</p> <p>Proved.</p> <p>Uh, okay, if you say so... Now, what's going on here line by line and term by term?</p> http://mathoverflow.net/questions/75804/how-to-prove-a-limit-exists-using-the-epsilon-delta-definition-of-a-limit/75807#75807 Answer by Joshua Green for How to prove a limit exists using the epsilon delta definition of a limit Joshua Green 2011-09-19T01:21:44Z 2011-09-19T01:21:44Z <p>We suspect that lim<sub><i>x</i>&rarr;1</sub> (<i>x</i> + 4) = 5, but how do we prove it?&nbsp; What does it <em>mean</em> for the limit to be 5?&nbsp; The definition is of the form "for every &epsilon; &gt; 0 there exists some &delta; > 0 such that ... ."&nbsp; To prove this, they choose an arbitrary &epsilon; &gt; 0 and look for a &delta; > 0 that has the desired property.</p> http://mathoverflow.net/questions/75804/how-to-prove-a-limit-exists-using-the-epsilon-delta-definition-of-a-limit/75811#75811 Answer by Free for How to prove a limit exists using the epsilon delta definition of a limit Free 2011-09-19T02:14:47Z 2011-09-19T02:14:47Z <p>Someone with editing powers, please delete my question. I appreciate having been directed to an appropriate forum. Thank you, folks.</p>