00:01
In this problem, we have been asked to evaluate the given limit if it exists.
00:04
We have the limit as x tends to negative 4, the square root of x squared plus 9 minus 5 divided by x plus 4.
00:14
Now, first of all, note that if we use direct substitution, then what do we get? we'll have the square root of negative 4 squared, which is 16 plus 9 minus 5 divided by negative 4 plus 4.
00:25
So we have the square root of 25 minus 5 divided by 0.
00:30
That's 5 minus 5 over 0 or 0 over 0.
00:34
0 over 0 is undefined.
00:37
So that just means that we cannot use direct substitution in this case.
00:41
So what we're going to do is we're going to rationalize the numerator.
00:46
So we have the square root of x square plus 9 minus 5 divided by x plus 4.
00:52
And what we're going to do is we're going to multiply this by the square root.
00:56
Of x squared plus 9 plus 5 divided by the square root of x squared plus 9 plus 5.
01:07
So what do we end up with? we have the limit as x tends to negative 4.
01:11
In the numerator, we're going to use the formula for a minus b times a plus b...