A Taylor Series is a mathematical tool used to approximate a non-polynomial function with a polynomial function. It allows for the calculation of complex functions by breaking them down into simpler terms.
The range of values in a Taylor Series is determined by the interval of convergence, which is the range of input values where the series will converge to the actual value of the function. This is typically determined using the ratio or root test.
No, a Taylor Series can only accurately represent a function within its interval of convergence. Outside of this range, the series may not converge to the actual value of the function and may provide inaccurate results.
The number of terms required for accurate representation varies for each function and depends on the desired level of precision. Generally, the more terms included, the more accurate the representation will be.
No, a Taylor Series can only approximate the value of a function. It becomes more accurate as more terms are included, but it will never give the exact value of the function.