![]() We will carefully walk through several examples of how to generate the Taylor Polynomial and see how to use it to approximate a function. We will start with the general formula for a Taylor Series, and recognize the specific pattern that is used. The general premise is that we start at a single point, and calculate an infinite number of derivatives knowing that the sum of these terms approximates the function itself. ![]() What a Taylor Polynomial does for us is to take something that is “hard” and turn it into something easier.Īs nicely stated by Wikipedia, Brook Taylor and Colin Maclaurin gave us such a way. The basic idea behind this lesson is that we like polynomials because they’re “easy” and we know how to differentiate and integrate them quickly. A Maclaurin Polynomial, is a special case of the Taylor Polynomial, that uses zero as our single point. The Taylor Series, or Taylor Polynomial, is a representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point. ![]() In this video lesson we will learn about the Taylor and Macluarin Series.
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