Arian.D said:-ln(1-x) I guess.
The Taylor Expansion is a mathematical representation of a function that can be used to approximate the behavior of that function at a specific point or interval. It is commonly used in calculus and other areas of mathematics to simplify complicated functions and make them easier to work with.
A Taylor Expansion can be useful because it allows us to approximate the behavior of a function at a particular point without having to directly evaluate the function at that point. This can save time and effort, especially when dealing with complex functions.
One limitation of a Taylor Expansion is that it is only an approximation of the behavior of a function, and may not accurately represent the function's behavior at points far from the point of expansion. Additionally, the accuracy of the approximation depends on the number of terms used in the expansion, so it may not be completely accurate.
A Taylor Expansion is calculated using derivatives of the function at the point of expansion. The formula for a Taylor Expansion is f(x) = f(a) + f'(a)(x-a) + (f''(a)/2!)(x-a)^2 + (f'''(a)/3!)(x-a)^3 + ... where a is the point of expansion and f'(a), f''(a), and f'''(a) are the first, second, and third derivatives of the function at that point, respectively.
A Taylor Expansion is used in various fields, such as physics, engineering, and economics, to approximate the behavior of real-world phenomena. For example, it can be used to model the trajectory of a projectile, the behavior of an electrical circuit, or the growth of a population. It is also used in computer graphics to create 3D images and animations.