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February 2001 - Volume 4, Issue 2

IN THIS ISSUE

Letter from the Editor
Calculator News
MathTip: Derivatives of Inverse Functions
Interview with James Vernon
Miscellany

LETTER FROM THE EDITOR

Unfortunately, the start to ticalc.org's new year hasn't been as good as we expected. Our file archivers have fallen behind a bit, but we'll try to make up lost ground as soon as possible.

This month I've interviewed James Vernon, the Aussie who's programmed such stuff like Alien Breed: Tower Assault.

CALCULATOR NEWS

The most exciting news this month has been the announcement of a new TI-83+. This new calculator will run at 15 Mhz and have 1.5 megs of FLASH ROM. It'll be available in April or May, and will be silver colored! Find more information at http://www.ti.com/calc/docs/83psilver.htm.

In program updates, Sean Kelly has released The Incredible Adventure, a new side-scroller. Matthew Roberts released Coaster 83+, a 3D roller coaster program. Flavien Racien released a new BomberMaze68K, and Julien Muchembled released new versions of his TIB Receiver, MaxMem, and HW2Patch programs for the TI-89/92+ to work with the new ROM version 2.05.

That's about it for this month.

MATHTIP: DERIVATIVES OF INVERSE FUNCTIONS

Have any of you ever had trouble remembered what the derivative of arctan(x) or arcsin(x) were? Then this tip is for you.

There's a wonderful bit of math theory called the Inverse Function Theorem. Quoting from Serge Lang's Undergraduate Analysis, the theorem states:

"Let f be continuous on the interval [a,b] and assume a < b. Assume that f is differentiable on the open interval a < x < b, and that f'(x) > 0 on this interval. Then the inverse function g of f, defined on [a',b'], is differentiable on the interval a' < y < b', and g'(y) = 1/f'(x) = 1/f'(g(y))."

See the book for a formal proof. So using this in an example:

d(tan(x),x) = 1 + (tan x)^2

By the theorem we expect

d(arctan(x),x) = 1 / ( 1 + (tan (arctan x))^2 )
= 1 / ( 1 + x^2 )

Which is indeed the derivative of arctan(x).

So, before you reach for your TI-89 and hit the derivative key, give this theorem a try.

At ticalc.org, we often receive many of the same questions. In this column, we hope to address some of these questions for a broader audience. If you'd like to submit a question, please email it to ask@ticalc.org.

Q: How come assembly programs don't work on my HW2 calculator running AMS 2.05?

A: To fix this problem, download the recently-released HW2Patch v2.30 by Julien Muchembled, available in the ticalc.org archives. Install this program, and assembly programs will now be compatible with your calculator. Good luck!

INTERVIEW WITH JAMES VERNON

Email: jimbob_v@hotmail.com

Interview Log