This post is to provide scripts to identify FIRST and LAST usages for a given date.

--How to get first day of a month 
Declare @Date Datetime = GETDATE()
SELECT DATEADD(month, DATEDIFF(month, 0, @date), 0);

--How to get Last day of a month 
Declare @Date Datetime = GETDATE()
SELECT DATEADD(DAY,-1,DATEADD(mm, DATEDIFF(m,0,@Date)+1,0));

--How to get first day of a Calendar Year 
DECLARE @DATE DATETIME = GETDATE()
SELECT DATEADD(YY, DATEDIFF(YY,0,@DATE), 0) AS STARTOFYEAR

--How to get Last day of a Calendar Year 
DECLARE @DATE DATETIME = GETDATE()
SELECT DATEADD(YY, DATEDIFF(YY,0,@DATE) + 1, -1) AS ENDOFYEAR

I will add more usages of FIRST/LAST day to the above list as I come across in future.