The City Council will hold its annual tax classification hearing at a special meeting Tuesday at 6 p.m. At the session, councilors will decide whether to continue the city’s current policy of having a split tax rate, and if so, how much of the residential tax burden to shift on to businesses. At its regular meeting Thursday, the council will consider adoption of two ordinances proposed by Mayor Ted Bettencourt. One would ban convicted Level 2 and 3 sex offenders from child safety zones,’ including parks, schools, libraries, and recreational centers; the other would create a new city position of business liaison. Also at Thursday’s meeting, which starts at 7:30 p.m., the council will hold a public hearing on an application by Peabody Monofill Associates for a special permit to remove 500,000 cubic yards of dirt and bedrock materials on Farm Avenue. Monofill had previously received a special permit but it has expired, according to city clerk Timothy Spanos. He said the firm is removing the material to create a private landfill at the site, near the former Peabody landfill. The council will hold a hearing into an application by 116 Main Street, LLC to increase the number of units allowed at a rental housing development there from nine to 11. Also on tap is a hearing into a special permit application by Total Outdoor Corp. to erect a 14-by-48-foot billboard at 108 Newbury St.. (Route 1).