00:01
We want to evaluate the limit of this expression as h approaches 0.
00:06
Now, if we try to directly substitute 0 in for h, we are going to get the indeterminate form of a limit.
00:15
We're going to get 0 over 0.
00:18
So let's see if that's really the case.
00:21
Plug in in 0 for h.
00:22
If h is 0, 2 plus 0 is 2, 2 cubed would be 8.
00:29
Okay so let's just write it down real quick okay if we just substitute zero in for h we would get two plus zero cubed minus eight over once again plugging in zero for eight so this would be zero well two plus zero is two two to the third is eight eight subtract eight is zero so we would have zero up top over zero so directly substituting in zero for h brings us to the indeterminate form of a limit zero over zero so basically we didn't get anywhere so in order to actually calculate this limit we are going to have to expand a numerator we're actually going to do 2 plus h to the third and which means 2 plus h times itself three times we're going to actually expand this and see if that helps us find the limit now 2 plus 2nd is going to be 8 plus 12h plus 6h squared plus h cubed so 2 plus h to the third is this expression right here we still have to write down to minus 8 and that whole thing that whole expression gets put over h in the denominator and let me fix this is supposed to be in l right here, so let's clean it up just a little bit.
02:59
Okay, so the limit of this expression as h approaches 0 is equal to the limit of this expression as h approaches zero.
03:08
Now, we can do a little bit of simplifying.
03:10
We have eight here, subtract eight there.
03:13
So those h will cancel.
03:17
And so we really had the limit of 12h plus 6h squared plus h cubed, all divided by h as h approaches zero.
03:24
Each of these terms has an h, has an h...