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myusernameis
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Homework Statement
how to you find like the answer for f(1.5), or f(1.00001) those kind of question? thanks
with like eq. = f(b)(x-b)... am i making sense? thanks
Dick said:You aren't being very specific. You write the taylor series for f(1+x) and put x=0.5 or x=0.00001. Does that make sense?
A Taylor series is a mathematical representation of a function as an infinite sum of terms, each of which is a polynomial of increasing degree. It is used to approximate the behavior of a function around a specific point.
A Taylor series is calculated using the derivatives of the function at a specific point. The general formula for a Taylor series is: f(x) = f(a) + f'(a)(x-a) + (f''(a)/2!)(x-a)^2 + ... + (fn(a)/n!)(x-a)^n
The purpose of a Taylor series is to approximate a function around a specific point. It allows us to represent a complex function with a simpler polynomial, making it easier to analyze and solve problems involving the function.
A Taylor series is a generalization of a Maclaurin series, which is a special case where the point of approximation is at x=0. In other words, a Maclaurin series is a Taylor series centered at x=0.
The accuracy of a Taylor series approximation depends on the number of terms used and the behavior of the function. In general, the more terms included in the series, the more accurate the approximation will be. However, there are cases where a Taylor series may not converge or may converge slowly, resulting in a less accurate approximation.