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This is a notation for limits.
So we're going to use our limit as H approaches zero of t + H /
7 * t + H + 2 - t / 7 T +2 all over H So the limit as H
approaches zero of t + H * 7 T plus 2 - t times the quantity
seven t + 7 H +2.
Just getting a common denominator here over seven t +
H + 2 times 7 T +2 and I'm going to bring that H into the
denominator where it's common.
Then we're going to distribute foil, combine like terms,
cancel, etcetera.
So the limit as H goes to zero of seven t ^2 + 2 T, +7 TH +2 H
minus seven t ^2 -, 7 TH -2 T Remember that everything without
an H net better cancel it this step.
If it doesn't, we have truly done something wrong.
So when I look here, here's a +2 T and a -2 T, here's a +7 T
squared and a -7 T squared, and all the other terms have a
single H in them.
So we're going to factor out that H and cancel it with the H
in the denominator.
So I'm going to end up with seven T + 2 - 7 T all over seven
T + H plus 2 * 7 T +2 when I put H going to 0.
Now we're going to get two over, oops, These terms back here
cancelled, but it didn't matter because they had an H in them,
so I just cancelled them now.
So we get 2 / 7 T +2.
Wow.
Seven t + 2 quantity squared.