let I be an interval in R, let f: I --> R and let c belong to I. suppose there exists a constant K and L such that |f(x) - L <= K|x-c| for x in I. show that the limit as x --> c of f(x) = L. I"m looking at this, but I dont know how to start. From what I know, this is very very familiar. the sentence ...."suppose there exists a constant K and L such that |f(x) - L| <= K|x-c|," doesn't this pretty much imply the statement? while I am doing practice problems, I always see this form and as soon as I find a delta and K, it pretty much assumes the answer. I feel that I am close, but I dont know how to go about it. maybe, let epsilon > 0, then we find a bound for |x - c|, and once we find K, this means |f(x) - L <= K|x-c|. then, we choose delta := inf(delta, 1/k*epsilon), then, if 0 < | x - c | < delta, it is proved.. close? way off? how about this one: lim as x to c, of root(x) = root(c) for c >0. how would I do that? can I square both sides? and have | x - c| < e?