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lim x→1 f(x) √x = 1. supposed to use the formal definition of limit to find the indicated limit regards

It says: Use the formal definition of limit to verify the indicated limit. lim x->1 1/x+1 = 1/2 in this sheet i got with answers, i dont understand the steps they're explaining so i would apreciate some kind of a newbie explanation since im not that good at absolute values. Regards