Try this:
$stmt = $mysqli->prepare("SELECT * FROM TABLENAME WHERE DATE=? ORDER BY ORDEBRYCOLUMN LIMIT ?, ?");
$date = "2014-05-11";
$stmt->bind_param('sii', $date, 0, 30);
$stmt->execute();
Bind params protect you from SQL injection attacks. If you put a variable directly into a SQL server string, someone can add more SQL to that string variable and run more sql queries than you want them to.