What is e?

Question

What is "e"? What does e stand for, what equations can it be used in? And what fields use it, what applications does it have? Just wondering. i know I've heard of e, but I have no idea what it is used for.

Thanks for explaining how it is found or derived. What can it be used for? How is it actually used in everyday life, or in careers? What exactly is it used to find?

Answer 1

e is a constant & e = 2.71828183.it is used in various mathematical equations and equations in physics.
it is used extensively in logarithms as the base.it is used in exponential functions

Answer 2

e^x is called the exponential function. Here x can be any real number like 0, -1, 1/2, pi, ...etc. When you plug in x=1, you get the number e.

The exponential function is a transcendental function, which basically means that you need to use an infinite series to describe the function.

e^x = 1 + x/1 + x^2/(1*2) + x^3/(1*2*3)....continue this pattern forever.

So to calculate the number e, you plug x = 1 into the infinite series above, and you get

e = 1 + 1+ 1/2 + 1/6 + 1/24 ....the more terms you take, the closer to the actual number e you get. You can never get an exact value of e in decimal form, because to do so, you would have to take and add an infinite number of fractions together which is impossible. For most applications you may only need to know e to 3 to 6 decimal places, but you can look up e to as many decimal places you want in tables that are probably accessible on the internet.

For a better explanation of how e is calculated, look here:

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/e.html

Hope this helps!

Answer 3

The number e (about 2.78) comes from calculus, and a pretty contrived explanation that I recall. Even good students in calc probably can't tell you - I'll try based on my recollection from about 10 yrs ago.

Take any number x. Now take one and divide by x, or just 1/x.

Graph that versus x. Say you want to find the area under that graph between say x = 2 and x =11. To do this exactly, you have to "integrate" 1/x and evaluate it at 11 and at 2 and subtract the result.

The "integral" of 1/x doesn't follow the normal formula used for other integrals. It is a special case. We call the integral of (1/x) the *natural log* of x, or ln(x) for short.

Wondering when I'll get to e?

Well e is the number than when you take the natural log of it, you get 1. So ln(e) = 1.

Totally unsatisfying - not nearly as nice as pi !

The number e shows up a lot in differential equations. If you take e and raise it to the y power, then you have e^y. The derivative of e^y is just e^y. The integral is the same too.

The usefulness of this is that it shows up in equations that predict motion and speed. For example, if z = e^(-t) is a common type of equation, where t is time, it means z is getting smaller and smaller as time goes on. At about 5 seconds, z is pretty close to zero.

Such an equation might describe, say, a washing machine slowing down after the spin cycle just ended.

Answer 4

Let's take the function f(x) = e^x. The number e raise to the exponent x. It has the property of being equal to it's growth rate.
i.e. d f(x)/dx = f(x). If in a two dimensional reference grid, we use polar coordinates instead of cartesian coordinate. The position of a point is given by the length of a line from the origin to the point (r) and the angle this line has relative to the x axis (theta) and we plot the function r(theta) = e^theta then you get a logarithmic spiral. This is the shape of spiral galaxies, water flushing in the toilet, hurricanes etc. The number e is as much important in mathematics than Pi.

Answer 5

"e" is the base for natual logarithms ....

it is the only number for which"

y = e^x
dy/dx = e^x ...

this is kinda cool

e = the sum from n= 0 to infinity of (1 / n!)

e = 1/0! + 1/1! + 1/2! + 1/3! ...

cool stuff ... and whenyou get to Taylor series and MAcLaurin expansions, you'll understand how this stuff works a bit better ....

"e" pops up all over the place in math and it sure makes life easier to have a pre-defined symbol for it

good luck

Answer 6

In my field, electronics, "e" represents Electromotive Force. It is expressed as Volts and is used in many equations dealing with current draw etc. Search Ohm's law and look at the associated equations.

Answer 7

It is the "base" of the natural logarithm function, which as I recall, is the function you get when you try to compute the area under the curve 1/x.

The number has numerous applications, mostly in engineering.

Answer 8

Electronic

Answer 9

I placed E in the calculator and I got: e = 2.71828183 ---> is that what you are speaking of?

Answer 10

http://en.wikipedia.org/wiki/E_%28mathematical_constant%29