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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