00:01
Here, we're given a function and we're asked to find the limit as x approaches negative 3 from both the right and left, and then also to discuss if it has a vertical asymptote.
00:11
Well, a vertical asymptote happens whenever the limit as x approaches that value from either the right or the left is either infinity or negative infinity.
00:20
And that will happen only if the denominator is equal to zero.
00:24
So to find any place that has a vertical asymptote, you just simply have to take the denominator x plus 3 and set it equal to zero.
00:30
When you do that, you're going to get x equals negative 3.
00:35
So x equals negative 3 is going to be the vertical asymptote.
00:39
And to prove that, let's go ahead and calculate these limits.
00:43
So if i calculate the limit from the left, that's that this first one is asking.
00:49
So that means that a value that's slightly less than negative 3.
00:53
So i'm going to have 1 over a number that is infinitely close to negative 3, but just a tiny bit less than negative 3.
01:04
So maybe it's negative 3 .1, or negative 3 .0001.
01:09
Well, when i add that to 3, we're going to essentially get 0 to the 5th.
01:15
However, because that number is slightly negative, i like to just draw a negative here...