What's Special about ' e ' ?

[thinktank]

I know e is defined as

Ltn->¥ (1 + 1/n)n


But why the heck it is like a magic number ?? What's Special about it ? {Other than being irrational }

Why is that

ò(1/x).dx = loge x

Why not Logarithm to any other base ??

[Sam Finch]

The point about e is that

http://161.58.186.97/attachment.php?s=&postid=650460

e^x is the only function that differentiates to make itself, which makes it very important in solving differential equations and calculus in general.

[Sam Finch]

we use this idea for the second part of your question to show

http://161.58.186.97/attachment.php?s=&postid=650462


hope this helps