NationStates Jolt Archive

Here. (http://en.wikipedia.org/math/9da4ec2806df4887a2ad6965b99434d3.png)

I am trying to explain how this represents "e" but I simply don't understand what that long line is.

Do you mean the integral sign?

Yes.

If you don't know what integrals are, I think that it's going to be very hard for you to understand that.

However, wikipedia has an explanation: http://en.wikipedia.org/wiki/Characterizations_of_the_exponential_function

It looks like an alternate definition of the natural logarithm. The long line is the definite integral operator

It's asking you to perform standard integration on that fuction from 1 to x.
http://en.wikipedia.org/wiki/Integral

Here. (http://en.wikipedia.org/math/9da4ec2806df4887a2ad6965b99434d3.png)

I am trying to explain how this represents "e" but I simply don't understand what that long line is.


the expression means if you make a graph of 1/x, 1 is equivalent to the area under the curve from x = 1 to x = e.

since that area is equivalent to ln(e), the solution of ln(x) = 1 is x = e.

Ahh! Thank you very much!