delta epsilon problem using precise definition of a limit?
I'm hoping someone can actually walk me through the steps of HOW this works, as opposed to just what to write down. I'm very very lost with this and hoping for some better insight than what's in the textbook!
Use the given graph of f(x) = √x to find a number δ that fulfills the following condition:
If absolute value(x-4) < delta then absolute value(sqrt(x)) - 2) < 0.4
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Start by re-writing it as
√(x) - 2 = (x-4) / (√(x) + 2)
so in particular
| √(x) - 2 | = |x-4| / |√(x) + 2|
. ≤ |x-4| / 2
where the last inequality is because
|√(x) + 2| ≥ 2
Can you see how to finish it?
Well if you divide first it would be easier