For example, you can get speed limits for boundary box(bbox parameter) from OpenStreetMaps using xapi overpass api.
But you should remember that data in OSM is not official and may be incomplete.
Example for Minsk:
https://www.overpass-api.de/api/xapi?*[maxspeed=*][bbox=5.6283473,50.5348043,5.6285261,50.534]
More info about xapi: https://wiki.openstreetmap.org/wiki/Xapi
Also you can use Overpass QL and gui tool to write your own requests and see data on the map:
https://overpass-turbo.eu/s/MMD