- #1
Callisto
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Hi
How do you expand
(1-exp(-1))^-1
as Taylor series
Callisto
How do you expand
(1-exp(-1))^-1
as Taylor series
Callisto
Last edited:
Taylor expansion is a mathematical concept that allows us to approximate a complex function using a simpler polynomial function. It is named after the mathematician Brook Taylor.
We use Taylor expansion to simplify complex functions and make them easier to work with. It also allows us to approximate values of a function at a certain point without having to know the exact function.
The formula for Taylor expansion is given by:
f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ... + f^n(a)(x-a)^n/n!
where f(x) is the function we want to approximate, a is the point around which we are approximating, and f'(a), f''(a), f'''(a), ..., f^n(a) are the derivatives of the function at point a.
Taylor series is the infinite expansion of a function, while Taylor expansion is a finite approximation of a function using a certain number of terms. Taylor series is used to represent an entire function, while Taylor expansion is used to approximate a function at a specific point.
Taylor expansion has various applications in fields such as physics, engineering, and economics. It is used to approximate solutions to differential equations, calculate derivatives and integrals, and make predictions in various scientific and mathematical models.