Series approximations are best used when a function is difficult to evaluate directly, particularly when it involves complex calculations or transcendental functions. They are particularly useful near a point where the function is well-behaved, such as around a point of convergence in Taylor or Maclaurin series. Additionally, series approximations are effective when a quick estimate is needed or when high precision is not required, allowing for simpler calculations while maintaining reasonable accuracy.
The best approximation is, of course, the exact value. A reasonable approximation is 106.
What approximation is "best" depends on the required level of accuracy.
Z Series are the best
It is 60
There is no "best" approximation. The square root is irrational and so it is a non-terminating, non-recurring decimal so adding one more digit will always make it a better approximation.
11.5326
20.1
20.1094005
When a periodic signal is approximated using a Fourier series, it is expressed as a sum of sinusoidal components (sines and cosines) with different frequencies, amplitudes, and phases. This approximation allows for the reconstruction of the original signal or an approximation of it over a specific interval. The accuracy of the approximation depends on the number of terms used in the series; more terms generally yield a closer representation of the original signal. However, at discontinuities, the approximation may exhibit Gibbs phenomenon, where oscillations occur near the discontinuities.
√40108 = 200.269817996
3.16227766 which is about 3.2
It can be used in function approximation, especially in physics and numerical analysis and system & signals. Actually, the essence is that the basis of series is orthorgonal.