# What is the Value of e-∞?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The number ‘e’ is known as Euler’s number which is an irrational number. It is a numerical constant having a value of 2.718281828459045..so on, or you can say e∞ is equal to ( 2.71…)∞. But when it is negative then the value of e-∞ is Zero. Learn why the value of e-∞ is 0.

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## The value of e-∞ is Zero and the value of e∞ is ( 2.71…)∞

Let us learn the explanation

Suppose X =e^(-infinity)

We can write it as X=1/e^infinity

When we multiply e infinite times with e, it will become very large that it will reach infinity

So, X=1/infinity

As infinity is a very large number and dividing 1 by a very large number gives a number very close to zero but not exactly zero.

So, X is a very small positive number as it reaches zero from positive side.

So, simply it is not zero because when e is increasing at a very high rate and it is tending towards a very large number and when e is raised to the -∞ then it becomes a very small number and hence tends to zero.

Summary:

## What is the Value of e-∞?

E, also known as Euler’s number, is an irrational number. The value of e∞ is ( 2.71…)∞, whereas, on the other hand, the value of e-∞ is Zero.

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