Why do we use e in math

Euler's number

We deal with Euler's number here. Let's look at this:

  • A Explanationwhat is Euler's number.
  • Examples to that particular number.
  • Tasks / exercises to this topic.
  • A Video in which Euler's number occurs.
  • A Question and answer area to this topic.

Tip: There are different constants in mathematics. Euler's number is one of them. However, the circle number Pi should be much better known.

Euler's number explanation

In mathematics there are so-called constants that can be used in equations. The circle number Pi is probably best known. Pi is needed, for example, to calculate the area of ​​a circle. This circle number is slightly larger than 3:

In addition to the circle number Pi, there is another constant that is very often used in mathematics. This is called Euler's number. In formulas / equations this is abbreviated with an "e". That number is slightly larger than 2.71.

example:

How big is x in the next equation?

Solution:

We substitute for e = 2.718282 and then solve the equation for x.

Display:

Euler's number application

What is Euler's number actually used for?

E function:

  • Functions can include Euler's number.
  • Example f (x) = ex.

Derive and integrate:

  • The so-called integral and differential calculus is dealt with in the 10th grade and in the upper grades.
  • One deals with the slope of a function or the area under a function.
  • In some cases, the E function can also occur with Euler's number.
  • The special thing about it is that "e" remains derived or integrated "e".

growth:

  • A number of growth processes (and also decay processes) in nature can be described with equations which contain the number "e".

physics:

  • Some processes in physics / technology involve functions that are based on "e".
  • For example in fluid dynamics.

logarithm:

  • The natural logarithm is the inverse of the E function.
  • You can find an example of this in the logarithmic equations.

Exercises / exercises Euler's number

Show:

Video E function

Application of Euler's number

The next video is about:

  • An application of Euler's number.
  • The E function is presented.
  • Examples for integrating the E function.
  • Various integration rules on the subject,

Next video »

Questions with answers Euler's number

In this section we look at typical questions with answers about Euler's number.


Q: How can you calculate Euler's number?

A: The number e was calculated by Leonhard Euler as the limit of the following series:

Q: When is the subject covered in school?

A: Euler's number is mostly dealt with in mathematics lessons from the 10th grade onwards. The E-function is also dealt with from the 10th grade as well as in the upper level and in many courses of study.