Re: TI-M: trig and continuity

To: ti-math@lists.ticalc.org
Subject: Re: TI-M: trig and continuity
From: Tony Morgan <gazzon@theoffspring.net>
Date: Wed, 08 Nov 2000 20:57:58 +0800
In-Reply-To: <20001106.145722.-411725.1.SkinneJ16@juno.com>
Reply-To: ti-math@lists.ticalc.org

At 02:57  6/11/00 -0800, you wrote:
>How can i find out where a function is discontinuous?  Lets take for
>example:
>f(x)=sin(x^2-2)?
>When i put it into my calculator using the zeros( function
>zeros(sin(x^2-2),x) the answer the calculator gives me is
>{when(@n2greater than or equal to the square root of (@n2*pi+2) and a
>whole bunch of other junk, am i doing it wrong? because the answer should
>be none.  Help, also if anybody has any programs for this and trigometric
>limits can you tell me where to get them?  Thanks a lot.
>
>Chris

Hrmmm, what you're saying, and what you're doing, seem to be two different 
things... let me explain.

First of all, the "zero" of a function is where the function crosses the 
x-axis (also called a 'root' or 'x-intercept') and has no bearing on the 
continuity of a function. The function f(x)=sin(x^2-2) has many roots. I 
don't have a spiffy ti-92 - just a plain 83 for me - but taking the easy 
route, if I simply graph the equation, I can see visually there are a large 
large number of zeroes.

However, your first question was how to find out where a function was 
discontinuous. You're correct - if you ask the calculator where the 
function f(x) (as above) is discontinous, it should reply 'nowhere', 
because that function is continuous over all real values of X.

But, since I don't have one of them spiffy ti-92 :( I can't really help you 
with your question - all I can do is tell you that "zeros(" is the wrong 
function to be using to test for continuity.

  -Tony

References:

TI-M: trig and continuity

From: Chris R Harrison <skinnej16@juno.com>