- #26

Thoth

^{ 2}and we want to see if there is a limit L=4 as x approaches c=2. At this point the problem might state that we want to choose a point so close to c that from x to c the absolute distance is three places of zero (δ=. 001) So we use the Limit definition and we found that |x-2|<. 001 or 1.999<x<2.001. Here we are approaching 2 from its left side (1.999) and from its right side (2.001).

We see that f (1.999)≈ 3.996 and f (2.001)≈ 4.004. So |f (x) –L| is 4.004-4= .004 and 3.996-4=-.004 hence ε= |. 004|=. 004 or ε=4σ

We see that as we approach point B from its left and from its right point B approaches a Limit number L from both directions then the limit exists and point B can be reached.

This is like saying that number 2 between number 1 and number 3 exists because if one approaches number 2 from number 1 (left side) or from number 3 (right side) one still reaches number 2.