posted by Anna .
Find the limit if it exists.
The limit of (sqrt(x+1)-2)/(x-3) as x tends to 3.
The limit of (sqrt(x+5)-sqrt(5))/x as x tends to 0
rationalize the numerator: I will do the first.
x+2-4=x-2 as x>3, it approaches 1
6+6-6-6 still zero.
so you have as the limit 1/0, it does not exist.