An intersection, or in this case, the much more limited radius of convergence, is the radius of convergence. You apply the same logic to domains of functions.
Finding the domain:
\(\to f(x) = \sin(\ln(x))\)
- The function \(\sin(x)\) has a domain of \((-\infty, \infty)\). \(\ln(x)\) is a domain name \("0, \infty"\).
- All values for which \(\ln(x) \ \ and\ \ \sin(x)\) both describe the domain of \(f(x)\). It must be in this scenario "\(0, \infty\)".
- \(f(x) = \sin(x) + \ln(x).\) The name of the website would be "\(0, \infty\)"
- Whenever you say a function does have a radius of convergence \((R)\), you're implying that all converge again for the following values:
- You say \(|x| < R\), but you also say \(|x| > R\).
- For \(|x| < 2.\), one function converges, while for \(|x| < 3\), the other converges.
- The most stringent are: \(|x| < 2.\)
- The total of the series' radius of convergence is: \(R=2\)
Find out more information about the radius of convergence here:
brainly.com/question/23558817
