Question

When looking through your discussions of Worksheets 6 and 7, there were two problems for which you all seemed to have some trouble. Both of these are reasonably easy to solve with the "sandwich theorem" that you saw on the previous worksheet There, we said that we needed to find functions flow, thi that are lower and upper bounds for f, and that that had to be the case for all ED. This works, but it is really not necessary: it just has to be the case in a neighborhood of . A formal statement of the theorem goes like this: Theorem: Let f:D → R be a function and I ED a point in the domain of the function. Let flow,fi be two functions that are also defined on D and that are continuous at T. Assume that there is a d so that flow(x) <f(x), VIE DU T - 8,7 + 8) and f(x) < fup(2), Assume furthermore that VrEDU (T - ,7 + 8). flow (T) = f(T) = fup(T). Then f is continuous at 7.

Answer 1

(x - 24 9-200 lee say 8=3 le flora i 2015! toine flow = $ gn5 = a no 1-ano na ako tana no tlano s foi & nE DO (2-8, 7+8) lim of law = 2 nañ eu 15277 5195 on sont & nyo fan fhigh & NED offens M -satnomal lim for no non ha fhigh = n2 T.sn theorem Scahned with Calm Scanner Mence by Sandwitch him sec (3 ja Alys