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