Chosen Solution
The MacBook Air 13" Mid 2011 doesn’t support Bluetooth 4.0. But an upgrade to “Bluetooth 2.1+EDR” is possible. The question is, is “Bluetooth 2.1 + EDR (Enhanced Data Rate)” possible the linkage(hand off, etcs) of the Mac and IOS?
Follow this: Continuity Activation Tool’ Enables Handoff on Older Macs
IMHO you’d have to use the activation tool to activate Continuity. But referring to your original question I’d like to mention that my MBA 12" Mid 2011 does BT Low energy being supported. AFAIK LE is part of the BT 4.x specification and doesn’t work with older versions. Thus I assume my MBA has BT 4.0 LE.
