00:01
Okay, so in this question we're asked to find these two limits.
00:04
So let's just get to it.
00:06
So first here, of course, we will simplify the denominator and the numerator.
00:11
So in this case, we get 2.
00:13
Then i have minus 14x plus 5x, so minus 14 plus 5 is minus 9.
00:22
And then we have minus 35 x squared on top.
00:29
And on the bottom we have 3.
00:32
Then we have minus 12 plus 2, it's minus 10 x, and then we have plus 2 times minus 1, minus 8 x squared.
00:42
Okay, and you should be able to read what the answer is going to be already from here.
00:45
I'm not going to stop here, but you should be able to see that at infinity, what matters are the terms of highest order, so the x squared, so the limit will be minus 35 over minus 8.
00:57
So 35 over 8 will be the solution, right? and the way to show that this is exactly what matters.
01:03
What we do is we divide or we factor out the highest order term on top and bottom.
01:10
So we factor out in x squared.
01:12
And this becomes 2 over x squared minus 9 over x minus 35 over same thing at the bottom.
01:21
So we have x squared.
01:23
And then we have 3 over x squared minus 10 over x minus 8...