Complex Numbers----e

 


You must have come across 'e' in many calculators, it's not just any other alphabet but actually a number! Just like pi! The Euler's number is one of the most popular numbers in math. It is an irrational number, it never ends and 'e' is a common way of denoting it's value of 2.182818284590..... 


Question

Suppose you have a box of chocolates and you drop them all on the floor, the probability of each chocolate going back in the wrong spot is 1/e! The more the chocolates, the closer the answer to 1/e!

Uses

'e' is used a lot in logarithms, it also has something to do with the 'ln' on your calculator. Practically, 'e' is used in data science, growth and population models, and physics amongst other concepts.


The Graph

When you differentiate a curve, you get an equation stating the gradient of every point on the curve, but when you differentiate a y=e^x curve, the gradient at any point will always be e^x!


The  f(x)=e^x graph never actually touches the x-axis! It is infinite.

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