ado1lz6 said:Why does f(x) = abs (0) not have the first Taylor polynomial center at Xo = 0 ?
Does it have second Taylor polynomial center at Xo = 0 ?
A Taylor Polynomial is a mathematical function used to approximate a given function at a specific point by using a series of derivatives. It can be thought of as a "best-fit" line or curve that closely follows the original function at that point.
The absolute value is used because it allows us to consider both positive and negative values when finding the center of the Taylor Polynomial. This is important because the Taylor Polynomial needs to be symmetrical around the center point in order to accurately approximate the original function.
The center of a Taylor Polynomial is determined by finding the value of x that makes the derivative of the original function equal to 0. This value is then used as the center point for the Taylor Polynomial.
The absolute value function, abs(x), is not differentiable at x=0 because the slope changes abruptly from negative to positive at this point. Therefore, when finding the center of the Taylor Polynomial, we must use the absolute value of x in order to consider both positive and negative values and find the appropriate center point.
No, Taylor Polynomials can only approximate the value of a function at a specific point. The accuracy of the approximation depends on the number of terms used in the polynomial and the smoothness of the original function. As the number of terms increases, the accuracy of the approximation also improves.