Shyan said:That just means you should expand around [itex] x=\pi [/itex] rather than the usual [itex] x=0 [/itex].
If you write [itex] f(a+\delta)=\sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!} \delta^n [/itex], then yes!TheRedDevil18 said:Does that mean the "a" value is pi ?
Yes, this is what the general term in your Taylor series will look like. Note that a Maclaurin series is a special case of a Taylor series, where a = 0.TheRedDevil18 said:I use this formula
f^(n)(a)*((x-a)^n)/n!
And sub in pi for a, thanks
A Taylor Series is a mathematical representation of a function as an infinite sum of terms. It is used to approximate a function by breaking it down into smaller, simpler parts.
A Taylor Series is calculated by finding the derivatives of a function at a specific point and plugging them into the formula for the Taylor Series. The formula is: f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...
The purpose of finding a Taylor Series is to approximate a function with a simpler, more manageable formula. This can be useful in solving difficult mathematical problems or analyzing functions that are too complex to work with directly.
A Taylor Series is a general form of a series expansion, while a Maclaurin Series is a special case of a Taylor Series where the point of expansion is at x=0. This means that the Maclaurin Series only uses non-negative powers of x, while a Taylor Series can use any power.
Taylor Series have many applications in mathematics, physics, and engineering. They are used to approximate functions in numerical analysis, to solve differential equations, and to study the behavior of functions in calculus. They are also used in signal processing, image processing, and many other fields.