[TI-M] Re: questions

To: <ti-math@lists.ticalc.org>
Subject: [TI-M] Re: questions
From: "Scott Noveck" <noveck@pluto.njcc.com>
Date: Fri, 23 Feb 2001 22:46:19 -0500
References: <20010223230324.4ACBE18018@mx-1.sollentuna.net>
Reply-To: ti-math@lists.ticalc.org

> ZoomFit adjusts yMin and yMax so that you can see the complete graph along
a
> given x-interval (determined by xMin and xMax).  Other than that...you
could
> try tracing the graph and pressing enter to center the window on that
portion
> of the graph.

I'm not sure what algorithm ZoomFit uses (to the original poster: it's in
the zoom menu), but I haven't always found it to be very good at giving a
window that's useful - I've gotten some really odd dimensions.

You could also write a program to do it, which might look something like
this (or it could be much more advanced, but this is sufficient for most
simple functions) although I can think of a few instances where this will be
wrong (where a relative min is greater than a relative max):

zoomwin()
prog
local xx1,xx2,yy1,yy2,zz1,zz2
zeros(y1(x),x)|x>-50 and x<50->zz1
if dim(z)[not equal sign]0 then
    zz1[0]-5->xx1
    zz1[dim(z)-1]+5->xx2
    zeros(d(y1(x)),x)|x>xx1 and x<xx2->zz2
    min(zz2)-5->yy1
    max(zz2)+5->yy2
    xx1->xmin
    xx2->xmax
    yy1->ymin
    yy2->ymax
endif
endprog

On second thought, I might find this program useful myself =)


> To graph conics (such as x^2 + y^2 = 7*y + 3), solve for y (use the solve
> function, I suggest) and replace +/- with {1,-1}.  Alternatively, you
could
> graph the resulting expressions for y separately.  For this particular
> equation, y = (+/-sqrt(61-4*x^2)+7)/2, so enter (in the y= editor) y1(x) =
> ({1,-1}*sqrt(61-4*x^2)+7)/2.

And if both you and solve(y1(x),y) cannot simply it down to a simple y=
equation, then you can set the equation equal to zero, go into the mode
dialog and choose 3d graph mode, then go to the graph, and diamond-bar for
format, choose style = implicit, and then enter the equation in terms of
both x and y to plot it implicitly (albeit slowly and with poor zoom
control).  If you want me to write a better explanation than that, just ask
=)

> For other implicitly defined functions, the manual explains how you can
use
> 3D graphing mode to graph an implicit function (I think you set to Contour
> Lines and set phi = pi/2, or soemthing like that...).  Page through it
until
> you see a graph that looks like a fence.

Just explained that above (poorly =)

> For 5*x + cos(x) = 0, there is only one (real) solution for x; x
= -.196164.
> I think the AMS software usually does a good job at finding most solutions
of
> equations like this, although I haven't used it much for that purpose.  As
> far as getting a decimal, I don't think equations like that have algebraic
> solutions...

You can use the "with" operator, the bar, to define constraints.  For
example, "solve(sin(x)=0,x)" gives you the general answer form, while
"solve(sin(x)=0,x)|x>=0 and x<=2pi" (you'll have to convert my ASCII
notation to calc notation) lists all of the answers in the interval 0 to 2pi

> Use the Var-Link menu to see what's in your calculator.  Even though
that's
> built-in, I suggest downloading TICT-Explorer (I'm not sure if it's
available
> specifically for the TI-92+...).

Yes, it is.

Alternatively, learn the math required to solve these yourself, like you're
supposed to, since this sounds a lot like those "how do i make my calculator
do all my tests for me?" questions. . .

    -Scott