2009 May « Community College Calculus

One Man Gathers What Another Man Spills

May 29, 2009 — vlorbik

$\bullet$ Dysfunctional Attitudes by Charles G&G Wells. Today’s “Handbook now online” post is big news: it appears at excited first glance to introduce a self-published masterpiece of math lexicography. What a guy.
$\bullet$ The repeated additon flap revisited by the Warrior.

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Triangles Too I Bet

May 29, 2009 — vlorbik

The Math Circle has a workshop coming up not far from here in July; sign me up. The chance to work with actual living schoolchildren is already probably worth the price of admission; working with the Kaplans… who can almost certainly teach me more in a day about the pop-mathbook racket than months of reading would… could turn out to be invaluable. But the main attraction is meeting at least one blogging correspondent.

I’m quitting Community College classroom teaching. It was one hell of a good run. For me, to have lived any other way would have been nuts. Thank you for your kind attention.

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Just Add Democracy

May 26, 2009 — vlorbik

Here’s smartt… a “Singapore Math” blog.

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Life Is Good

May 25, 2009 — vlorbik

This glossary by Pat Ballew has a lot of info! I’d've posted this link already except that, um, I thought I already had. No time to take notes! Read! Read! Read!

Also, hours later, here’s a statistical lexicon spotted at the Endeavour.

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Cleanup Time

May 23, 2009 — vlorbik

$\bullet$ The Calculus Wars reviewed (the May Notices).
$\bullet$ What the heck, an opinion piece in the same issue (calculators).
$\bullet$ Just read the contents every issue. There’s always something interesting.

For instance that editorial led me to F. Quinn’s Essays on Mathematics Education.

Posted in Links, Mathwars, Notices. 1 Comment »

Untargeted Tutoring

May 22, 2009 — vlorbik

$\bullet$ A Noted Scholar’s glossary; a partial index of S&M Defeated mathposts.
$\bullet$ What Reformers Really Mean. Also “CSR” at ed.gov.

In other news, I’ve marked some popular VME posts (under the blogroll at right).

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Looks Good On Paper

May 21, 2009 — vlorbik

$\bullet$ A practice test for prospective math teachers (in Massachusetts) from Prentice. Found in this ghastly video-ridden Boston Globe piece, via M.A. Chandler‘s Washington Post mathblog.
$\bullet$ “One Step Ahead of the Train Wreck” that is Everyday Mathematics (Barry G via KTM).

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Last Quarter’s Final

May 19, 2009 — vlorbik

1. Let $f(x) = {1\over{x^2}}$ . Compute $f'(x)$ using the definition (the limit of a difference quotient).

2. Differentiate (find $D_x(f)$ ):
a. $f(x) = 5^{3x}$

b. $f(x) = \log_2(x^3)$

c. $f(x) = \arctan({1\over x})$

3. Find formulas for $y'$ using a. logarithmic differentiation and b. the “Quotient Rule”, where $= {{(2x+1)^2}\over x}$ .

4. Evaluate the limits (where defined; “DNE” for any that are not):
a. $\lim_{x\rightarrow 3}{{x-3}\over{|x-3|}}$
b. $\lim_{x\rightarrow \infty} {{3x^2 + 5x - 11}\over{2x^2 + 7}}$
c. $\lim_{x\rightarrow 0} {{e^x-1}\over{e^{2x}-1}}$

5. Find the equation of the line tangent to g(x) = ln(x) at x = 1.

6. Use implicit differentiation to find ${{dy}\over{dx}}$ given that $y = e^{xy} + x^2$ .

7. Find an algebraic formula for cos(arctan(x)) using a sketch of a right triangle.

8. Compute the second derivative, ${{d^2 y}\over{dx^2}}$ , where $y = \sin(x) + xe^x$ .

9. A balloon rises at a rate of 10 feet per second from a point on the ground 100 feet from an observer. Find the rate of change of the angle of elevation of the balloon from the observer when the balloon is 100 feet off the ground.

10. Find (both co-ordinates of) the local extrema and inflection point for the cubic function $y = x^3 - 9x - 27$ . Sketch the curve.

11. Estimate $\root3\of{123}$ using a tangent line approximation (hint: $\root3\of{125} = 5$ ).

12. Find the antiderivatives.
a. $\int {1\over{x^2 +1}}dx$
b. $\int x^3 dx$
c. $\int dx$

Exercises. Answers go in comments.
Marry, sir. Find all the typos.
Moreover. Convince a skeptic that problem 1 or one much like it is worth learning how to do (and belongs on a Calc I final) even if they know $f'(x) = {{-2}\over{x^3}}$ . Hint: even a god-damn computer knows that; this is a course for college credit.
Secondarily. Explain why one does not go on, “Harvard Calculus” style, to require discussions about graphs (without calculations)… I thought this was a course for college credit. For extra credit, justify the lack of an “epsilon-delta” proof on this test.
Sixth and lastly. Were notations for differentiation ( ${{dy}\over{dx}}, f'(x), D_x (f)$ ) just tossed around at random to confuse everyone? Or what? Justify your conclusions.
Thirdly. How in the name of the nameless name is it even remotely possible that after using TeX for seventeen freaking years, Vlorbik doesn’t know how to typeset those limits properly? For that matter, why didn’t he just scan last year’s test and upload the S.O.B.? How can one survive without being able to work the most basic tools?
Explain why, despite having been present on two or more occasions when Vlorbik explained how to do the tangent line problem on the calculator with no calculus whatsoever, students will blank out on problem 5. No, that’s easy. Explain why they think we made up a whole new symbol for the natural log when we really meant the reciprocal function… now that’s a mystery. And why should it be hard to recognize a constant function, for hecksake? What’s up with these people who haven’t learned calculus yet? Why don’t they get it?