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>> [music] Welcome back to Calculus One
and welcome to Week 7 of our time

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together.
We've been at this for a while already and

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much of the time that we spent thus far
has just been on the mechanics of how to

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calculate derivitaves.
Looking ahead, we've got three weeks now

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to really focus in on why you'd want to
calculate derivatives, applications, or

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differentiation.
This week, in Week 7, we've got two

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applications lined up.
The first is L'Hopital's rule.

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It's a way to evaluate limits by using
derivatives.

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And it allows you to calculate limits that
would be very hard to calculate without

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access to L'hopital's Rule.
The second application this week is

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related rates.
There's a ton of situations in the real

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world where you've got two things, and
they're changing together.

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And you want to know if one thing is
changing at some speed, say, how fast is

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the other thing changing?
There's rates of change and you want to

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know how they're related.
Well, I hope you enjoy these applications.

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We've got two more weeks after these
sub-applications.

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If you've got questions, be sure to post
your questions on the forum, or come and

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talk to us at office hours.
Good luck.