What is significant about e?

Question

anonymous · Answer

|dw:1370591523328:dw|

parthkohli · Answer

$$\dfrac{\partial}{\partial x} a^x = a^x \log_e a  $$The fact that the natural log and not any other log base comes up is very interesting.

parthkohli · Answer

$Ce^x$ is the only function with a constant derivative.

zzr0ck3r · Answer

it is its own derivative!

zzr0ck3r · Answer

I don't think constant derivative is the right way to say it...

zzr0ck3r · Answer

you cant do differential equations without it:)

zzr0ck3r · Answer

$$e^{I*\pi} + 1 = 0$$

parthkohli · Answer

That's another way to say it lol

$1$ is its own square, cube and its own square root, cube root.
$e^x$ is its own second, third derivative and is its own second, third integral.

So if $1$ is the king of arithmetic, then $e^x$ is the king of the functions!

zzr0ck3r · Answer

lol hah that is great

zzr0ck3r · Answer

e was the first letter in Eulers name!

zzr0ck3r · Answer

I can do this all day

parthkohli · Answer

lol

zzr0ck3r · Answer

there are many significant, its irrational.
^^I hope someone gets that

zzr0ck3r · Answer

we are nerds Parth

zzr0ck3r · Answer

:)

parthkohli · Answer

And it's the real compounding: the continuous compounding. 

If you keep 1 dollar in a bank and it keeps compounding 1% at each instant, then the amount in the bank after $1$ year will be $e$.

parthkohli · Answer

The longer the instant, the more you are more way off $e$

parthkohli · Answer

$e$ is also transcendental. :-D

zzr0ck3r · Answer

I with I could give you another medal:P

parthkohli · Answer

lol

anonymous · Answer

e^it = cost + isint

zzr0ck3r · Answer

now simplify

parthkohli · Answer

That one too!

zzr0ck3r · Answer

$$e^{i\pi}=1$$

zzr0ck3r · Answer

that's the same thing, hes repeating:P

anonymous · Answer

it = it

zzr0ck3r · Answer

$$e^{2i\pi}=-1$$

anonymous · Answer

omfg can someone tell goformit100 to stop asking stupid questions

zzr0ck3r · Answer

this one is cooler, it has the first prime, addition, multiplication,exponential....

parthkohli · Answer

$$e^x = 1 + x + \dfrac{x^2}{2} + \dfrac{x^3}{6} + \cdots$$

parthkohli · Answer

$$e^{2\pi i} + 1 = 0$$:-D

zzr0ck3r · Answer

and thus we know $$\int\limits e^{x^{2}}dx$$

anonymous · Answer

You can solve that using alternative numbering systems

zzr0ck3r · Answer

there are many ways, but the coolest is expansion imo

anonymous · Answer

x^x^x^x^x? I had to do that back when I was a freshman in math 55 LOL

anonymous · Answer

Take the derivative of it..took like an hour

zzr0ck3r · Answer

lol

zzr0ck3r · Answer

no ty