Quandaries
and Queries
What is the limit as x approaches 3 of
(sqrt(x+1)-2)/(x-3).
I'm having a lot of difficulty figuring this one out algebraically as you don't have to ratonalize the denominator.
Please help.Thank you very much.
Hi Abraham,
I would rrationalize the numerator by multiplying both the numerator and denominator by sqrt(x+1)-2.
This gives a numerator of
[sqrt(x+1)-2][sqrt(x+1)+2]
= [sqrt(x+1)]2 -22
= x + 1 - 4 = x - 3
and a denominator of
(x - 3)[sqrt(x+1)+1]
Since x is not 3 you can cancel the (x-3)Factors and get
1/[sqrt(x+1)+2]
Penny