Does MBA early 2014 base model support 3440 x 1440 (WQHD ultrawide 21:9) external monitor? Can a MacBook Air (13-inch, Early 2014) 1.4 GHz Intel Core i5, 4 GB 1600 MHz DDR3, Intel HD Graphics 5000 1536 MB support external display over displayport input displaying a 3440 x 1440 resolution at 60Hz ? 

P.S: Planning to purchase a WQHD monitor and run it above mentioned mac book air.
Yes, Flawlessly!!!! in the image there is a lie the  2560 x 1080 is not 34-inches is 25-inches and that one is connected trough display link usb-hdmi adapter from toshiba, the 3440 x 1440 is 34-inches but you need thunderbolt cable, the macbook air early 2014 can run them both! Super happy!!! to the toshiba adapter I can even plug another 1920 x 1080, so I wonder if through daisy chain it can run two 34 inch... well the answer is yes!!