To diagnose domain name resolution issues, running dig +trace example.com or nslookup example.com can provide detailed information about the entire process of resolving a domain name, from the root servers down to the authoritative name servers. Comparing this output with known good output can reveal any discrepancies or failures in the resolution process. If dig +trace or nslookup provides the correct information, this indicates that the issue is intermittent or specific to the server's resolver configuration rather than a problem with the DNS server itself. Modifying /etc/resolv.conf would not fully diagnose the problem, as it could be a configuration issue, and checking for a high number of outgoing DNS queries or pinging the domain would not yield detailed resolution process information. Therefore, using dig (with the +trace option) or nslookup is the best initial step for diagnosis.