f(x) = x^2 and we want to show that as x -> a, f(x) -> a^2.(adsbygoogle = window.adsbygoogle || []).push({});

So, we must ensure that |x^2 - a^2| < eps.

The book (Calculus by Spivak) starts of by bounding |x - a| < 1 which leads us to

|x + a| < 2|a| + 1.

This is the part where I get lost:

I can understand that we require |x - a| < eps/ (2|a| + 1),

but

why do we choose |x - a| < min(1, eps/ (2|a| + 1)) ?

And what happens if min(1, eps/ (2|a| + 1)) = 1 ?

Thank you very much for your help in advance! :)

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# Basic limit question ( f(x) = x^2 )

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