1. ## infinite limit

Hello,
I do not understand this...

Determine the infinite limit:

lim x-->-3+ f(x); f(x) = x+2/x+3

I looked at the numerator and denominator...

(x+2) approaches -1 as x gets closer to -3 from the right and
(x+3) approchaes 0 as x gets closer to -3 from the right

How do I know that the function f(x) has an limit of negative infinity?
How do I know that the limit is infinite at all? (Why not just "does not exist")

Thanks

2. Originally Posted by DBA
Hello,
I do not understand this...

Determine the infinite limit:

lim x-->-3+ f(x); f(x) = x+2/x+3

I looked at the numerator and denominator...

(x+2) approaches -1 as x gets closer to -3 from the right and
(x+3) approchaes 0 as x gets closer to -3 from the right

How do I know that the function f(x) has an limit of negative infinity?
How do I know that the limit is infinite at all? (Why not just "does not exist")

Thanks
You have $\lim_{x \rightarrow -3^+} \frac{x+2}{x+3}$.

$\frac{x+2}{x+3} = 1 - \frac{1}{x + 3}$ and it should be clear from a graph of $y = 1 - \frac{1}{x+3}$ that $\lim_{x \rightarrow -3^+} \left( 1 - \frac{1}{x+3} \right) = - \infty$.

This is different from $\lim_{x \rightarrow -3} \left( 1 - \frac{1}{x+3} \right)$, which does not exist because the left hand limit is not equal to the right hand limit.

3. Thanks you for the answer. But my problem is it, to define the limit without a graph.
With a graph I can see in which direction the infinity goes, but without that, how can I see if it is negative or positive infinity?

Thanks