Transcription of Solving epsilon-delta problems
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Solving epsilon-delta problems
Solving epsilon - delta problemsMath 1A, 313,315 DISS eptember 29, 2014 There will probably be at least one epsilon - delta problem on the midterm and the kind of problems ask you to show1thatlimx af(x) =Lfor some particularfand particularL,using the actual definition of limits in terms of sand srather than the limit laws. For example , there might be a question asking you toshow thatlimx a7x+ 3 = 7a+ 3(1)orlimx 5x2 x 1 = 19,(2)using the definition of a The rules of the gameNormally, the answer to this kind of question will be of the following form:Given >0, let = [something positive, usually depending on anda]. If0<|x a|< then [some series of steps goes here], so|f(x) L|< .Some examples of this are Examples 2-4 of section Note that [some series of steps goeshere] should consist of a proof that|f(x) L|< , from the assumptions that >0 is whatever we said it was, and 0<|x a|< . , prove1In these kind of problems , much of the work goes into figuring out what should of this work is shown in the actual answer.
These kind of problems ask you to show1 that lim x!a f(x) = L for some particular fand particular L, using the actual de nition of limits in terms of ’s and ’s rather than the limit laws. For example, there might be a question asking you to show that lim x!a 7x+ 3 = 7a+ 3 (1) or lim x!5 x2 x 1 = 19; (2) using the de nition of a limit. 1 The ...
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