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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].

2 Common mistakes From looking through people’s homework, I got the impression that the following mistakes were common: Dividing by zero, or treating 1as if it were an actual number. Writing things like lim x!1 x4 1 x 1 = x3 + x2 + x+ 1 = 4: In lim x!1 x4 1 x 1, the variable xis a bound variable. To paraphrase Wikipedia, \there is nothing ...

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