Find an open interval about a on which the inequality | f(x) - L | < E holds. Then give a value for D > 0 such that for all x satisfying 0 < | x - a | < D the inequality | f(x) - L | < E holds.(adsbygoogle = window.adsbygoogle || []).push({});

f(x) = x^2, L = 4, a = -2, E = .5

To solve I setup the inequality

Step 1: -.5 < x^2 - 4 < .5

Step 2: 3.5 < x^2 < 4.5

This is where I get stuck, need help with the algebra.

I got sqrt 3.5 < x < sqrt 4.5 & thought my interval for E would equal (sqrt 3.5, sqrt 4.5), but the book gives (-sqrt 4.5, -sqrt 3.5). I know if you take the sqrt, you have to take the positive & the negative of that number, but how do you know which to choose in this case & by doing this, does the inequality signs always reverse (like < to >)? Going to skip the rest of the problem, because I didn't have a problem solving the rest.

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# Homework Help: Finding Delta

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