In the world of mathematics, there are fascinating concepts that lead us into the realm of limits and infinite possibilities. One such concept is finding the value of ‘e’ raised to the power of negative infinity, denoted as ‘e^-∞.’

In this article, we will break down the steps to calculate the value of e^-∞ and uncover its mathematical significance.

What is the value of e^-∞?

The expression ‘e^-∞‘ represents the limit of ‘e’ as it approaches negative infinity.

lim_x→−∞​e^x

As ‘x’ approaches negative infinity, ‘e^x‘ approaches zero:

lim_x→−∞​e^x= 0

This is because ‘​e^x‘ represents exponential growth, and as ‘x’ becomes more and more negative, the value of ‘​e^x‘ gets closer and closer to zero.

So, the value of ‘e^-∞‘ is 0.

In summary, ‘e^-∞‘ represents the limit of ‘e^x‘ as ‘x’ approaches negative infinity, and this limit is equal to 0. This mathematical concept is essential in understanding how exponential functions behave as their exponent becomes infinitely negative.