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Proof of a Limit

raees

Hi can someone please help with this.

I have the following question:

The solution is given in two parts..

part 1 -->

btw this is 'figure 2.23' -->

and this is part 2 -->

I understand the entire solution except the last part in part 2, where it tries to prove for epsilon as being greater than or equal to 4.. could someone explain that part please

bump

What more precisely don't you get?

Repeat the first argument (where they consider epsilon smaller than 4) but when you get to the line

4 - epsilon < x^2 < 4 + epsilon

note that this implies

0 < x^2 < 4 + epsilon

since you are assuming that epsilon is greater than 4. Now continue with the rest of the argument as for epsilon < 4 making the appropriate subsequent changes following on from that.