Table of contents

What is e on a calculator? – e to the xHow to put e in a calculator? Calculate e to the xe calculator – examplesFAQsAre you solving an equation with Euler's number? Our * e* calculator is here to help! Our tool allows you to compute

*e*

**to the power of any number you desire**.

**Keep on reading** if you're still wondering what exactly Euler's number is, **what does e mean on a calculator**, and how to calculate

*e*to the

*x*📐🧑🏫

🙋 You can also explore the exponential functions of other bases with our exponent calculator.

## What is e on a calculator? – e to the x

*e* is one of the most important constants in mathematics. We cannot write *e* as a fraction with integer numerator and denominator, and **its decimal expansion is infinite and non-periodic** – just like the famous number *π*. Its value **is equal to 2.7182818284590452353602…** and counting! (This is where rounding and approximation become essential.) 🧮

Now that we know what *e* (also known as **Euler's number**) and its approximate value is, we can start thinking about its possible applications.

*e*is the**base**of the natural logarithm, the same you can find using natural log calculator.We use

*e*in the*natural*exponential function (**eˣ**= e power x).In the

**eˣ**function, the slope of the tangent line to**any point on the graph**is equal to its y-coordinate at that point.**(1 + 1/n)ⁿ**is the sequence that we use to estimate the value of*e*.**The sequence gets closer to**. When*e*the larger*n*is*n = infinity*, the sequence value is equal to Euler's number.We use this equation in compound interest calculations.

*e*is equal to the result of the following factorial sum:

$\scriptsize\qquad\frac{1}{0!} + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \ldots$0!1+1!1+2!1+3!1+4!1+5!1+…

*e*is also a part of**the most beautiful**equation in mathematics: $e^{iπ} + 1 = 0$eiπ+1=0 🌺

**Since we already know what's the Euler's number, how about some other numbers we use in physics?**

- Biot number;
- Knudsen number;
- Avogadro's number;
- Reynolds number; and
- f-number 😀

🔎 To see the real-life applications of exponential functions, head to Omni's exponential growth calculator.

## How to put e in a calculator? Calculate e to the x

Since we're forced to use an approximation of *e*, we can simply **input the value of e into any calculator**.

**How does it work in practice? How to calculate e to the power x?**

If your calculator doesn't allow symbols, simply enter **2.718281828** (or any rounded form of this number) into your choice value box 👍

## e calculator – examples

In this section, we'll answer the very big question: "**How to calculate e to the power x?**" using both our calculator and the traditional formula.

**The**– it's so simple it doesn't need further explanation. Enter the value of*e*calculator**x**into the text box and enjoy your results displayed alongside the**step-by-step solution**👣The traditional calculation requires you to choose

**how many decimal places of the Euler's number you will use**.

We decided to use **9 decimal places**.

**Let's follow an example:**

We know that the area up to any x-value is also equal to *e*ˣ:

We'd love to calculate the area up to the *e*¹⁰ function.

*e*¹⁰ = 2.718281828¹⁰;2.718281828¹⁰ = 2.718281828 × 2.718281828 × 2.718281828 × …;

2.718281828¹⁰ = 22026.47.

And this is how to calculate e to the power of 10.

As you can see, calculating *e* to the power of x might be pretty troublesome and time-consuming – **our tool is a simple solution** for that unnecessary problem 🤗

### What does exp mean?

"Exp" is short for "exponential" and is used in the notation **exp(x)** as another way to write **eˣ**.

### How do you calculate e to the power x without calculator?

You can use the following Taylor series approximation: **eˣ = 1 + x + x²/2! + x³/3! + …**. Continue calculating and adding terms to get a better approximation.

### What is e to the negative infinity?

**Zero.** Let's say we have **e ^{-N}**, where

**N**is a large number tending toward infinity. Now, given that

**e**, as

^{-N}= 1/e^{N}**N**gets larger,

**e**will get smaller, ending up at zero if

^{-N}**N = ∞**.

### What is the derivative of e to the x?

The derivative of ** eˣ** is itself,

**. Here is a step-by-step proof:**

*e*ˣ- The equation
can be rewritten as*y*=*e*ˣ**ln**.*y*=*x* - Differentiate both sides of this equation and use the chain rule:
**1/***y*× d*y*/d*x*= 1**d***y*/d*x*=*y* - Since
, therefore*y*=*e*ˣ**d**.*y*/d*x*=*e*ˣ

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