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?
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...
Let e > 0 be given.
Choose d = e.
0 < | x-1 | < d = e
| (x+4) - 5 | < e
| f(x) - L | < e
Uh, okay, if you say so... Now, what's going on here line by line and term by term?