Taylor Series

Many functions can be written as powers series about some point of their domain. About a point aa (say) we get
f(a+h)=f(a)+11!f(a)h+12!f(a)h2+13!f(a)h3+...f(a + h) = f(a) + \large\frac{1}{1!}\normalsize f'(a)h + \large\frac{1}{2!}\normalsize f''(a)h^{2} + \large\frac{1}{3!}\normalsize f'''(a)h^{3} + ...
which we call the Taylor series of ff.

The case a=0a=0 is known as the Maclaurin series of ff.

The Taylor Series for sin(x)\sin(x) and cos(x)\cos(x) are shown below.