Re: TI-M: Limits
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Re: TI-M: Limits
In a message dated 10/9/00 8:14:16 PM Mountain Daylight Time,
skinnej16@juno.com writes:
> I was wondering if someone could shed some light on limits for me? I
> want to know 2 things how to do it by yourself and then how to do it on
> the 89. So how would you figure a limit out in your head, for example,
> find the limit of f(x)= (x-1)/(x^3-2) when x approaches x. How do you
> know that it is 1/3? I get that on the 89, but i want to know how to do
> it without becuase i don't want to get lost in calculus and we are just
> begining limits. Now how would i get an answer on my calculator, like
> this. lim (x+1)/(x^3-1) x is approaching 1+(but the positive is a
> superscript)? when i put in my calculator like this
> lim((x-1)/(x^3-1),x,1,positive) i get undef but the answer is supposed to
> be +infinity. What am I doing wrong?
[ f(x) = (x+1)/(x^3-1) ]
On the 89, do lim(f(x),x,1,<any positive number>) for the limit as x -> 1
from the right.
In your head...well you could use this reasoning:
The places where f(x) is undefined would be where the denominator equals 0;
in this case, f(1) = undef. For x > 1, both the numerator and denominator of
f(x) are positive, so f(x) > 0 for x > 1. The other critical points for f(x)
are when f(x) = 0; in this case, f(-1) = 0. It should be obvious that for -1
< x < 1, f(x) < 0; for x < -1, f(x) > 0.
That's the best answer I can give... :)
JayEll