Why does my calculator tell me -1/(0^2) = -infinity. How is this different from 1/0?
1/0 isn't anything, since 1/x approaches infinity if x --> 0 from the right (x>0) and 1/x approaches -infinity if x --> 0 from the left (x<0).
By contrast, -1/x^2 is always negative, so it approaches negative infinity as x --> 0 no matter which direction you come from.
Bear in mind, I'm not saying that -1/0^2 equals - infinity. It's not really defined actually.
What kind of calculator are you using anyway? Mine always says "error - divide by 0" if I put in 1/0.
I think his question is why his calculator (TI-89) says 1/0 is undefined but 1/02 says infinity.
It just has to do with how the calculator calculates things I guess.
Edit: I tried it for other powers and it seems like a/0n is given as infinity for even n and "undef" for odd n if n is positive.
If n is negative it gives a/0n as 0. If n is zero it gives it as a, but writes a warning message saying that 00 was replaced by 1.
Edit: I think latex is broken...
...and I agree, Latex is broken.
Never trust your calculator for mathematical 'subtleties' like this, use your mind
Incidnetally, the function
does have a continuous extension to x=0 in the extended real numbers. Whereas
That makes sense. The calculator is probably computing the limit of those functions as they go to 0, which is infinity for even functions and undefined for odd.
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