+0  
 
0
540
2
avatar+1191 

Can somebody give me a good explanation on Euler's number?

DarkBlaze347  May 17, 2015

Best Answer 

 #2
avatar+93691 
+15

Here is another link

http://www.askamathematician.com/2013/01/q-what-makes-natural-logarithms-natural-whats-so-special-about-the-number-e/

 

I don't pretend to understand this very well myself but one very important quality of e is that if you graph $$y=e^x$$ on the number plane then the gradient of the tangent to the curve at any point is also    $$e^x$$

 

In terms of calculus this means that if

$$\\y=e^x\;\;then\\
y'=e^x\quad too.$$

 

Also

e^x = \lim_{n \rightarrow \infty} \left(1 + \frac{x}{n}\right)^n

This is a very important fact when dealing with continuous exponential growth and decay.

 

Here is another site

http://en.wikipedia.org/wiki/Exponential_function

Melody  May 18, 2015
 #1
avatar+90056 
+13

Here you go, DB.......not too difficult to understand, I don't think.......

 

http://www.mathsisfun.com/numbers/e-eulers-number.html

 

 

CPhill  May 17, 2015
 #2
avatar+93691 
+15
Best Answer

Here is another link

http://www.askamathematician.com/2013/01/q-what-makes-natural-logarithms-natural-whats-so-special-about-the-number-e/

 

I don't pretend to understand this very well myself but one very important quality of e is that if you graph $$y=e^x$$ on the number plane then the gradient of the tangent to the curve at any point is also    $$e^x$$

 

In terms of calculus this means that if

$$\\y=e^x\;\;then\\
y'=e^x\quad too.$$

 

Also

e^x = \lim_{n \rightarrow \infty} \left(1 + \frac{x}{n}\right)^n

This is a very important fact when dealing with continuous exponential growth and decay.

 

Here is another site

http://en.wikipedia.org/wiki/Exponential_function

Melody  May 18, 2015

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