MAT 21A Lecture Notes - Lecture 6: Joule
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MAT 21A Full Course Notes
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Steps for stuff: math 21a, 2016 fall. 10-3-2016: rigorous de nition for limits: limx a f(x) = l if the following is true: given > 0, we can nd (in terms of ) such that. 0 < |x a| < |f(x) l| < : if there is a that makes the above implication hold, then so does any positive constant smaller than . Take the following steps: (1) formulate the problem: given > 0, we want to nd > 0 such that. 0 < |x a| < |f(x) l| < . (2) start with |f(x) l| < and come up with an inequality in the form |x a| < . |g(x)| for some function |g(x)|. (remarks: factorization can usually help accomplish this. |g(x)| by nding a number m such that |x a| < step. The next goal to get rid of m .
