Using Taylor even when Maclaurin converges everywhere
- Author:
- Lenore Horner
- Topic:
- Calculus
Just because the series representation converges everywhere doesn't mean it converges rapidly everywhere. The graph below illustrates this. Note that if the series is shifted by pi/2 then we can use the memorized Maclaurin series for the cosine function but with shifted x values and write out the representation almost as quickly as if we used the also-memorized Maclaurin series for the sine.