This is the fall 2012 Math 90 Introductory Calculus I posthead for David Lowry’s TA sections (which should be those in section 1 with Hulse). **This is not the main site for the whole course** (which can be found at https://sites.google.com/a/brown.edu/fa12-math0090/), but it will contain helpful bits and is a good venue through which you can ask questions.

In particular, the posts that have been put up so far can be found under the Math 90 tag category. **If this is your first time visiting, and you are one of my students, please go to the Math 90: Week 1 page and leave a comment.**

Here are links to the pages themselves:

- Week 1
- Week 2
- Week 3
- Week 4
- Week 5
- Week 7 (including test solutions)
- Week 8 (and the separate quiz solutions)
- Week 10
- Week 11 (including test solutions)
- Concluding Remarks

And now, the administrative details (the rest can be found on the main course website).

TA Name: David Lowry

email address: djlowry [at] math [dot] brown.edu (although please only use email for private communication – math questions can be asked here, and others can benefit from their openness).

Instructor Name: Thomas Hulse

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I have a question about #16 waaaay back from section 3.9 (inverse trig)

lim as x–>(-)infinity of arctan(x)

I got this one wrong on my homework, and am confused as to how the answer is -(pi/3). I thought the answer would have to be somewhere where there is a vertical asymptote, or where cos=0.

Inverse trig is sort of hard to handle, and I understand the confusion, especially if you were led to believe that the answer is $latex -pi/3$. The correct answer is $latex – pi/2$, which is when $latex cos theta = 0$ as you mentioned.

To repeat, $latex lim_{x to -infty} arctan x = – pi/2$.

Reading your question, it sounds as though you were going along the right paths of reasoning too – looking at the graph of $latex tan x$, you expect the answer to be at a vertical asymptote, and in particular the asymptote where the “standard portion” of the tangent curve (the one that passes through the origin) goes to $latex – infty$.

Does that make sense?

yes, it makes sense. Although I am also a bit confused about why (+)pi/2 doesn’t work, as there is an asymptote there, and it looks like the asymptotes are going to both pos. and neg. infinity?

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