# Sky(e) is the limit

#### Using e as an introduction to limits

Limits are an interesting concept. Being new to this myself, I was trying to visualise this to understand the core concept.

## What are limits?

Suppose, you're a equation of variable *That* number is the limit.

It's like the more you try to resist your urge to eat an ice-cream, the closer you get to actually eating one. (That's my visualisation.)

## e as a limit

Let's take an expression:

This looks awfully similar to the equation of :Compound Interest; because it kinda is.

But what happens if you start chugging in numbers to

... we see that it is getting closer and closer to the :Euler's Constant!

Really fascinating! I suppose all the smug businessmen will leave their shops and start doing Calculus after seeing this.

### To actually see it happening

I made a Python script to plug in values of x in increments, and I could really **see** it happening. This helped a lot in *empirically* understanding the concept.

```
from sympy import * # This package allows you to do complex mathematical equations
iteration = 0 # where x = iterations
while True:
iteration += 1000 # increments
n = symbols("n")
expression = (1+1/n)**n # (1+1/x)^x
number = limit(expression, n, iteration)
print(f"When n = {iteration} -> {float(form)}") # Prints result
```

So yea, there you go. There are fun stuff happening in Maths (and all around the world), and once we get exposed to it, there's no going back.

Happy Practicing!

### :x Euler's Constant

It is a mathematical constant **2.718281828**... named after mathematician Leonhard Euler. Something like the

This comes in handy in Logarithm as well.

### :x Compound Interest

Where:

- A is the Compound Amount
- P is the Principal Amount
- I is the Interest Rate
- N is the no. of times interest is compounded
*per year* - T is the no. of years.

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