<p>Do people actually understand this proofs? Or more like WHY they do it the way they do? Or they just learn the mechanical way of solving the problems and just chug it out on the exams? Because I've been going over this crap for the last 2 days and it still seems incomprehensible to me. At least I understand WHY for the linear equations, but quadratic equations seems impossible to understand.. pls help!!</p>
<p>how often are they tested on? and is math mostly like these on the upper division?</p>
<p>Delta-epsilon proofs are very simple conceptually, but sometimes people aren’t use to the amount of freedom you get when proving something.</p>
<p>Basically, given any epsilon arbitrarily small, |f(x) - L| can be made less than epsilon by making |x-c|<delta.</p>
<p>In other words, I can make f(x) arbitrarily close to L by making by making x closer and closer to c.</p>
<p>In order to show this, we have to make a connection between |f(x)-L| and |x-c|. For linear equations this is usually pretty simple. If f(x) has powers of x greater than one, then you have to do some tricky stuff like requiring |x-c| smaller than a random number and then taking the minimum of whatever number you chose and whatever relationship you get with epsilon. Reading that over, I realize it’s pretty incoherent. There are probably people who can explain it better than I can.</p>
<p>I would do an example, but this forum does support LaTex so it would be illegible.</p>