For a given epsilon e > 0, I need to find a delta d such that for all x, abs(x) < d.
I have these three:
abs(sqrt(x+4) - 2) < e
For this, I rationalized abs(sqrt(x+4) - 2) and got abs(x/(sqrt(x+4)+2), which I said is <= abs(x/2). Then I chose delta to be e/2. Is this ok?
The second one is abs(((1-x)^4) - 1) < e and the third one is abs([(x^2 - x + 1)/(x+1)] - 1) < e. I'm not really sure how to do these. Could someone show me how to find the appropriate d(e)? I'm somewhat lost at the moment and I have a whole bunch to solve.