Having trouble following the logic of this proof

38 Views Asked by At

I'm confused about

  1. The highlighted portion
  2. The logic of the proof thereafter. Thanks.

enter image description here

enter image description here

1

There are 1 best solutions below

2
On

The reason why we could choose a bound of $\mid x - 2\mid$ is that the limit is a local feature. We could only consider the case where $x$ is near $2$. How we choose $\delta$ here is simple to consider the restriction that we mentioned earlier and to make sure the difference is less than $\epsilon$.