Is |Epsilon|= |"something"| x |Delta|?

[DigitalSplendid]

Help appreciated on if anything wrong done above and how to proceed further so as to solve the given problem.

 

[jonah2.0]

Beer induced hack reaction follows.

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View attachment 39122

Help appreciated on if anything wrong done above and how to proceed further so as to solve the given problem.

If \(\displaystyle \delta < 1\) then \(\displaystyle |2x^2 − 2| = 2|x − 1||x + 1| < 6|x − 1| < \epsilon\) if \(\displaystyle |x − 1| < \epsilon/6\), so \(\displaystyle \delta\) = min\(\displaystyle (1, \epsilon/6)\).