00:01
For problem 60, the actual question is in problem 32, and it's a limit of x square minus 100 divided by x minus 10 as x goes to 10.
00:22
See the trouble when x is exactly at 10, you're going to have a division by zero.
00:29
So normally, if they want you to use a table, but the shortcut so that you can double check your answer before we do the table is, let's, because this is a polynomial, let's just factorize and simplify the whole equation.
00:47
This is x minus 10 times x plus 10, right? i'm just rewriting the whole equation divided by x minus 10.
01:02
So now we can get rid of x minus 10 here and x minus 10 here, right? and we can say, but we have to write the condition that this only works for x different from 10.
01:21
It cannot be 10.
01:22
So for that, we have then simplified the limit to limit of x plus 10 as x as x approaches.
01:39
10.
01:40
So this works for everything x different than 10.
01:46
So if you're doing it was a table, this equation makes it easier than you know, like having x squared minus 100 divided by x minus 10.
01:57
Well, you have different values of, you know, x.
02:03
So if you're for the table, let's say, you know, now we can say x and then we have x plus 10 right which is the value of the actual function so let's say when x equals close to 10 from the negative side which is less than 10 let's say 9 .9 then x plus 10 is just 19 .9 you don't even need a calculator how easy and then let's do 9 .99 that would be a 19 .9.
02:44
So you get the idea.
02:46
And then let's do from the other side, which would be since 10 .1, then here we have 20 .1.
02:56
If we do 10 .01, this will be 20 .01.
03:07
So you can keep doing this, but you don't have to.
03:10
All we want to see is the trend from the negative side in the positive side are about 20...