Is Microsoft SQL server 2008 sp2 supported for the Content broker database in SDL Tridion 2011 sp1?
Microsoft SQL Server 2008 R2 SP1 is supported for SDL Tridion 2011 SP1. SQL Server 2008 R2 is supported but deprecated (support for it is dropped in the next releases of SDL Tridion). This (and more) information can be found in the online documentation (requires login).
The Hotfix rollup, or SDL Tridion 2011 SP1 HR2 added support for Microsoft SQL Server 2008 R2 SP2. The actual version Microsoft SQL Server 2008 SP2 was never supported for 2011.