The domain of the arctan power series is limited to values of x that fall within a range of -1 to 1. This is because the arctan function only exists for values between -1 and 1, and the power series is used to approximate the arctan function.
If x is outside the domain of arctan power series, the power series will not be able to accurately approximate the value of arctan for that x value. This is because the power series is only a valid representation of the arctan function within the specified domain of -1 to 1.
The domain of arctan power series is important because it determines the range of values for which the power series can accurately approximate the arctan function. If the domain is not strictly adhered to, the approximation will not be accurate and may lead to incorrect results.
No, the domain of arctan power series cannot be expanded. The arctan function only exists for values between -1 and 1, and the power series is used to approximate this function. Attempting to expand the domain would result in inaccurate approximations.
No, there are no exceptions to the domain of arctan power series. The domain is a fundamental aspect of the power series and cannot be altered without compromising the accuracy of the approximation. It is important to adhere to the specified domain when using the arctan power series.