00:01
Question 20 asks to determine the limit graphically and then to confirm algebraically.
00:06
So when we graph t squared minus 3t plus 2 divided by t squared minus 4, we can see that as t approaches 2 from the left and t approaches 2 from the right, the limit is at 1 4th.
00:25
And we can confirm this algebraically.
00:27
So let's do this on the next page.
00:29
So we're trying to find the limit as t approaches 2 of t squared minus 3t plus 2 divided by t squared minus 4.
00:43
Obviously, we cannot do this by substitution because if we were to put 2 in the denominator, it'll be 4 minus 4 and we cannot divide by a 0.
00:54
So what we can do instead is actually rewrite the numerator and the denominator.
00:59
So when we factor t squared minus 3 t plus 2, it'll be, oh did not right there, with t minus 2 times t minus 1, divided by t minus 2 times t plus 2.
01:19
As you can see automatically we can cancel out these two factors.
01:27
And now we're left with, i'm going to write down here, limit as t approaches to, of t minus 1 in numerator and t plus 2 in the denominator...