I purchased my 2011 Mustang MCA edition used it has the 3.7 V-6
How can I tell if it has limited slip rear end??

 

This is from Wikipedia. According to them it has a limited slip. (see highlighted red text below)

Also, turn off the traction control (if equipped) and do a burnout. Do you get one tire or two spinning?

2011–2012
New powertrains for 2011 replaced the aging 4.0 L V6 used in the Mustang since the 2005 model year. These include Ford's Duratec 37 3.7 L DOHC V6. Unlike earlier versions of the engine, the 2011 Mustang features Twin-independent Variable Cam Timing (Ti-VCT). The new V6 now has true dual exhaust, compared to the single outlet exhaust that the previous 4.0 L V6 – the engine is rated to produce 305 bhp (227 kW) @ 6500rpm and 280 lb·ft (380 N·m) of torque @ 4250rpm.[23]
The 2011 Mustang is also capable of achieving good fuel efficiency due in part to also-new transmissions. With the newly standard Getrag MT82 6-speed manual transmission co-developed with Ford, the 2011 Mustang has been rated by the EPA to achieve 19 mpg-US (12 L/100 km; 23 mpg-imp) in city driving and 29 mpg-US (8.1 L/100 km; 35 mpg-imp) on the highway. The newly optional Ford 6R60 6-speed automatic achieves 19 mpg-US (12 L/100 km; 23 mpg-imp) in city and 31 mpg-US (7.6 L/100 km; 37 mpg-imp) on the highway.[24] The a newly standard 2.73:1 limited slip rear axle is more fuel efficient compared to the more aggressive 3.31:1 axle used previously. The 3.31:1 axle remains available in the 2011 Mustang as a performance option.[23]
The 2011 Mustang offered a V6 Performance Package starting in summer 2010. The package features a standard 3.31:1 rear axle, stiffer suspension tuning, 19-inch wheels with performance tires, a strut tower brace, and performance-oriented electronic stability control calibration.[23]
Other, non-powertrain related upgrades made to the 2011 Mustang include a Nexteer Automotive Electric Power Steering (EPS) system with pull-drift compensation and active nibble control, general aerodynamic and NVH improvements over the 2010 Mustang, a digital message/information center, blind spot mirrors integrated into the car's side mirrors, a universal garage door opener, a 160 mph speedometer, and Ford's MyKey programmable vehicle key technology.[23]

 

Starting in 2011 all Mustangs got the 8.8" rear end with the tlok.

 

Thank you!!