Want this question answered?
Yes. If the Maclaurin expansion of a function locally converges to the function, then you know the function is smooth. In addition, if the residual of the Maclaurin expansion converges to 0, the function is analytic.
Best example is that an "odd" (or "even") function's Maclaurin series only has terms with odd (or even) powers. cos(x) and sin(x) are examples of odd and even functions with easy to calculate Maclaurin series.
who discovered in arithmetic series
yes a discontinuous function can be developed in a fourier series
A company called Alexander Proudfoot Mining developed the Reactivity Series as a way of summarising all the different properties of the reactive metals as they were involved in extracting metals from ore
mechnical properties of hardened steel
no every function cannot be expressed in fourier series... fourier series can b usd only for periodic functions.
The legend is the function that identifies the data marker for each series in a chart.
Yes, a Fourier series can be used to approximate a function with some discontinuities. This can be proved easily.
Series in calculus are important for many reasons. One of them is the ability to differentiate or integrate a series that represents a function much easier than the function itself.
On the Nova V Series II, episode I
It wasn't discovered and was created as a series of stops going north for the escaping slaves.