# How did they compute this e equation?

In summary, the value of e was discovered by Swiss mathematician Leonhard Euler in the 18th century. It is considered one of the most important mathematical constants and has connections to many areas of mathematics. The value of e can be approximated using a series expansion or by using a calculator or computer program. It is often used in exponential functions because of its relation to exponential growth and its useful properties. Additionally, e is the base of the natural logarithm function and is used to solve equations involving exponential and logarithmic functions.

## Homework Statement

this is a question I'm working on, and there's this step I'm stuck on
it looks like this:

## The Attempt at a Solution

how come the 9.8 became the 50?

thanks

$$\int e^{ax}dx= \frac{1}{a}e^{ax}+C$$

rock.freak667 said:
$$\int e^{ax}dx= \frac{1}{a}e^{ax}+C$$

ohhHHHH ... it seems all simple now

thanks!

## 1. How did scientists discover the value of e?

The value of e was first discovered by Swiss mathematician Leonhard Euler in the 18th century. He found that the limit of (1 + 1/n)^n as n approaches infinity was a constant value, which we now know as e.

## 2. What is the significance of e in mathematics?

Euler's number, or e, is considered one of the most important mathematical constants. It has connections to many areas of mathematics, including calculus, number theory, and complex analysis. It also has practical applications in fields such as finance and physics.

## 3. How is the value of e calculated?

The value of e can be approximated using a series expansion or by using a calculator or computer program that has e as a predefined constant. It is an irrational number, meaning it cannot be expressed as a simple fraction, so its decimal representation goes on infinitely.

## 4. Why is e often used in exponential functions?

The value of e is closely related to the concept of exponential growth, making it a natural choice for the base of exponential functions. It also has several useful properties that make it a convenient choice in mathematical equations.

## 5. How does e relate to natural logarithms?

Euler's number, e, is the base of the natural logarithm function. This means that e^x is the inverse function of ln(x), and they are used to solve equations involving exponential and logarithmic functions. The value of e is also used in the definition of the derivative of the natural logarithm.

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