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rexregisanimi
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How would one expand f+df about x? I'm messing something up in the process and can't seem to resolve it lol
rexregisanimi said:It shouldn't matter; f is a function of x (and other variables)...
It does matter. Letters without any definition are pointless.rexregisanimi said:It shouldn't matter;
The Taylor Expansion of f+df About x is a mathematical technique used to approximate a function f(x) with a polynomial of increasing degree centered at a specific point x. This expansion is useful in finding the values of a function at points near the initial point x.
The Taylor Expansion of f+df About x can be calculated using the Taylor series formula, which is f(x) = f(x0) + f'(x0)(x-x0) + (1/2!)f''(x0)(x-x0)^2 + (1/3!)f'''(x0)(x-x0)^3 + ... where x0 is the point we are approximating around and f'(x0), f''(x0), and f'''(x0) are the derivatives of the function evaluated at x0.
The purpose of using the Taylor Expansion of f+df About x is to obtain an approximation of a function at a specific point x. This can be useful in situations where it is difficult to find the exact value of a function or when the function is too complex to work with directly.
The Taylor Expansion of f+df About x is used in various fields such as physics, engineering, and economics. It is used to approximate the behavior of a system or to find the values of functions in these fields. For example, it can be used to approximate the trajectory of a projectile or to predict the growth of a population.
The Taylor Expansion of f+df About x involves adding a small change (df) to the original function (f) before performing the expansion. This allows for a more accurate approximation of the function at a specific point x. On the other hand, the Taylor Expansion of f About x only uses the original function f and does not take into account any small changes. Therefore, the Taylor Expansion of f+df About x is generally more accurate than the Taylor Expansion of f About x.