1 Divided by zero

Started by King Kandy3 pages
King Kandy Senior Member

Originally posted by lord xyz
1/x integrated is in theory, 1/0 (x^-1 becomes (x^0)/0)

but in reality it's ln(x).

I don't know what to make of this.


Where in the world did you get that notion? the antiderivative of X^-1 would just be X^0, or zero. Not X^0/0. However because all constants derive to zero, x^0 does as well, so ln(x) is the integral.

lord xyz Restricted

x^0=1 for all numbers but 0.

Bardock42 Junior Member

Kid's right.

Anyways, this explains why the derivative of ln(x) is 1/x

http://www.ltcconline.net/greenl/courses/116/ExpLog/logDerivative.htm

King Kandy Senior Member

Originally posted by lord xyz
x^0=1 for all numbers but 0.

That was a typo, I meant to say X^0 or ONE, not X^0 or zero.

lord xyz Restricted

The way I was taught calculus was the rule for integrating:

add one to the power, then divide by the power.

differentiation is the inverse.

King Kandy Senior Member

That somewhat works (however not in this situation, the dividing part is to cancel coefficients which doesn't apply here), but that doesn't work for 1/x, because even though you could conceivably see the integral as 0, the derivative of 0 is most certainly not 1/x.

Bardock42 Junior Member

Originally posted by lord xyz
The way I was taught calculus was the rule for integrating:

add one to the power, then divide by the power.

differentiation is the inverse.

Yeah, that's not a general rule though. Just a convenient way to find many integrals.