Mathematics 1560 Lecture 2: c2s3
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2. 3 the precise de nition of a limit (read this section of the text! These are the most important 7 pages in this 1200 page book!) Let f (x) be de ned on an open interval about x0, except possibly at x0 itself. Prove for f (x) = mx + b, m 6= 0, that lim x a f (x) = f (a). Page 82 number 12, page 83 numbers 20 and 40. If limx c f (x) = l and limx c g(x) = m, then then limx c(f (x) + g(x)) = l + m. We wish to prove limx c(f (x) + g(x)) = l + m under the assump- tions limx c f (x) = l and limx c g(x) = m. let > 0 be given. Then /2 > 0 and there exists 1 > 0 such that for all x with 0 < |x c| < 1 we have |f (x) l| < /2.
