Calculus › Section J · Infinite series › Topic J.10
Taylor and Maclaurin series
Take the Taylor polynomial from the approximation topic and never stop adding terms: the result is a power series that can equal the whole function. This is the library of series that mathematics actually runs on.
In this topic
- From polynomial to infinite series
- Convergence is part of the answer
- Worked example: eˣ and the number e
- Worked example: sine and cosine
- The library to memorise
- Building by substitution
- Worked example: a series with no antiderivative
- Worked example: ln x at a new centre
- The binomial series
- Common mistakes to avoid
- Key takeaways
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Standards: 10 (BC)