Day 9 in MAT229

Today:

• Announcements:
  • Heard from Simon that the Math/Stat lab has been closed when it should have been open. I've got an email out to our chair, to find out what's going on.

  • Last time I deduced $\cos^{-1}(x)$ in terms of $\sin^{-1}(x)$. One can also define $\tan^{-1}(x)$ in terms of $\sin^{-1}(x)$, as shown in this Mathematica file. "All you need is sine!" (doo doo, doo doo doo....)
  • We do have an exam next week, Tuesday. It's good to get one in early.

• Today we get serious with section 6.8 -- indeterminate forms. So here we go: it's about limits:
  • 6.8 -- indeterminate forms
    • As noted before, the limit definition of the derivative is perhaps our most important example. We'll use the alternative form of that definition today, to motivate L'Hôpital's rule.

      Notice how I wrote that: your text has a nice discussion of this. It was evidently originally spelled like a large dispensory of societal healthcare, but I don't like using that form because it may make mathematicians pronounce it incorrectly.... So "L'Hôpital" it is!

  • 6.8 -- indeterminate forms worksheet