calculus
posted by Anna on .
Find the limit if it exists.
The limit of (sqrt(x+1)2)/(x3) 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+24=x2 as x>3, it approaches 1
Denominator: ((x3)(sqrt(x+1)+2)
xsqrt(x+1)+2x3sqrt(x+1)6
as x>3
3sqrt4+63sqrt(4)6
6+666 still zero.
so you have as the limit 1/0, it does not exist.