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.
Numerator: (sqrt(x+1)-2)(sqrt(x+1)+2_
x+2-4=x-2 as x>3, it approaches 1
Denominator: ((x-3)(sqrt(x+1)+2)
xsqrt(x+1)+2x-3sqrt(x+1)-6
as x>3
3sqrt4+6-3sqrt(4)-6
6+6-6-6 still zero.
so you have as the limit 1/0, it does not exist.