Question

find the limit. use L'Hopital's Rule if necessary.

lim (x^2+3x+2)/(x^2+1)
x -> -1

Answer 1

In this case you don't need L'Hopital's Rule. The denominator is not zero at x = -1
The function equals 0/2 = 0 at x=-1

Answer 2

So you just plug -1 into the equation to get the limit?

Answer 3

isn't there a way you do it with the derivatives?

Answer 4

Joe, you dont' always have to use Calculus to do Limit questions, just like drwls said.

The first thing I do is sub the approach value into your expression, there are three possilbilities:
1. your get a real number as an answer as above, 0/2 is real.
That is the answer to that limit, write it down and you are done.
2. you get a/0, where a is not equal to zero.
This is undefined, and there is no limit .
3. you get 0/0
This is the classic case and that is where the Calculus comes in.
You may try to factor it, if it is a simple algebraic expression, I can guarantee you it will factor.
If the expression is transcendental, that is it contains logs, trig or some other weird mathematical operation you might want to use L'Hopital's rule