Timeline for Interesting but very easy epsilon-delta problems?
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| Feb 24, 2018 at 18:33 | comment | added | user52817 | @DaveRenfro..indeed so. As you know, the "cheat" works for any polynomial, and reduces the challenge of finding a $\delta$ to the algorithm of calculating $A=\sum_{k=1}^n|c_k|$ where $c_k$ are the Taylor coefficients $c_k=\frac{f^{(k)}(x_0)}{k!}$. If $|x-x_0|<1$ then $\delta=\frac{\epsilon}{A}$ works. | |
| Feb 23, 2018 at 18:20 | comment | added | Dave L Renfro | FYI, I've seen this method used as an application of Taylor series expansions. See my 19 August 2001 sci.math post How to cheat with polynomial epsilon/delta proofs. Incidentally, in the same thread Gerald A. Edgar shows how one can easily get the same expansion by school algebra --- for your example, replace $x$ with $y + 4,$ then expand the result in powers of $y,$ then in that expansion replace $y$ with $x - 4.$ | |
| Feb 23, 2018 at 17:10 | history | answered | user52817 | CC BY-SA 3.0 |