What is e?? 😲 Euler number 2.718 #maths #calculus

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[Srijan-q]

Bro if n tends to infinity means n is a very big number and when 1 will divided by this big number then 1/n will tend to zero so 1 +1/n will be approx 1 so 1^n= 1 only. bro till i can understand but when it will tend to infinity i can't understand brother plz help me🙏

[Samir-zbxk]

Three main definitions of e:

-lim(x-->∞) of (1+1/x)^x
-Infinite sum of reciprocal factorials
-The number "b" such that d/dx[b^x]=b^x

[ANIMX_FLAME]

E is the rate in which anything grows exponentially in the expanding universe

1)It is used with Mantissa in scientific notation.
2)It can be used to represent growth of an organism just like bacteria
3) It is used in writing exponent form of a floating literal or real literal in java

[aman_raj]

e = 1 + 1/(1!) + 1/(2!) + 1/(3!) + 1/(4!)

Another method!💀👍

[leandrobayonito]

Thankies.
Math is not intimidating.
The mathematics classroom sessions with faculty members suck in teaching.

This illustration finally shed light on us.

[shikikankillzone]

*_"Do not go home until you finish reading the value of E"_*

[mazmuz]

As mathematics student, this help me a lot before choosing complex analysis subject

[AlainVerse]

e is also the solution to the integral equation:

x
/ 1÷x dx = 1
1

[anonymouscheesepie]

e is defined as the number _A_ such that d/dx(A^x) = A^x.

[CLASHERHERE]

Also 1/x
lim (1+x) = e
n->0

[parthhooda]

Energy
A number such that derivative of its exponent is itself
The definition you showed
The 5th letter of alphabet
mc²
Electric field
Electrons are denoted by e
Charge on an electron is denoted by e

[jacobstarr]

e=limit of (1+x)^(1/x) as x goes to 0.
e=Σ1/n! starting from n=0 to infinity.
e=limit of (1+1/x)^x as x goes to infinity.
e is the number such that ln(e)=1.
e is the number such that when graphed exponentially, it’s height is equal to its slope.

[foxypiratecove]

Just, e is denoted using `\mathrm{e}` because it's a mathematical constant.

[amanjangid]

indeterminate form 1^(infinity) (where 1 is actually tending to 1 and that infinity is actually tending to infinity) has a general solution


if when x tends to a, f(x) tends to 1 and g(x) tends to infinity
then, lim(x tends to a) (f(x))^g(x) = e^n
where n = lim(x tends to a) (f(x) - 1).g(x)

so, here, lim(n tends to infinity) ((1 + 1/n))^n = e^k
where k = lim(n tends to infinity) (1 + 1/n - 1).n = 1
so, "e" is the answer to that

[Justkidding]

- In physics, "E" often represents energy, with variations such as kinetic energy (KE) and potential energy (PE).
- In mathematics, "E" can represent the exponential function, often denoted as "exp(x)" or "e^x".
- In computer science, "E" might denote the complexity class "EXP, " representing problems solvable in exponential time.
- In chemistry, "E" can represent an electrode potential in electrochemistry.
- In economics, "E" might stand for elasticity, a measure of responsiveness of one variable to changes in another.
- In biology, "E" could represent the enzyme, a biological catalyst facilitating chemical reactions.
- In finance, "E" might refer to earnings, often used in calculations such as price-to-earnings ratios (P/E).
- In engineering, "E" could stand for modulus of elasticity, a measure of a material's stiffness.
-E is eulurs number

[leonardhofstadter]

Wow thats a great way to see that. Thanks a lot

[bicycleshelter]

E is the solution to lim n->0 (x^n - 1)/n or more commonly know in this case as the d/dx (f(x)) = (f(x)) * 1

[FFGAMER-cqyq]

Bro e is the most clever way of making the maximum or minimum(max. Or min, are commonly used for finding derivatives, ; what is derivatives ? Derivative is the slope of a function a particular point, ; then what does the slope do? I tells us how is y changing w.r.t. x . ;why do we need this ? It tells us the instantaneous rate of change .
Didn't get it, dont worry.
Example÷
Say the distance travelled by a car on a highway is given by the f(x)= x³.m where x is time
So after 1 second, distance travelled by car = 1 m
After 2 sec= 8m
After 3 sec= 27m
After 4 sec= 64m
As we can observe that the speed of car is changing (increasing), because the distance travelled in a unit time is not constant.
Suppose we want to find the Speed of car 🚗 at x=3 .
So how do we do this ?
How does the speedometer do this ?
The speedometer has total distance which has been travelled by car at x=3sec it let the car to move for a slightest of the sec say, 0.0001 sec.
It then gets the distance traveled by it in this period .viz. (3+0.0001)³
It then finds the difference in the distance traveled by .
speed at x = 3 sec. ( very precise)
=( 3+0.0001)³-3³ / 0.0001
= 27.0009 m/s )
I highly recommend you to download Desmos and draw the graph .
You will find the at 3 and 3.0001 this curved graph becomes a straight.)
Similar we use e to find the derivative (slope of the tangent at a point of a function which tells us the rate of change, in distance -time graph it tells us the speed at x=. Any point you like )
Of an exponential function
Like 2^x or 3^x.

Hope you like it.❤

[rupinderrupinder]

e is also known as coefficient of restitution

[TengkuAlam]

i think the most relatable definition is the derivative of exp(x) is itself, then we can find many from there, for example the series representation, euler identity and many more