What is e^infinity?

The value of e raised to the power of infinity, written as e^∞, is not a defined number. In mathematics, infinity is not a specific number, but rather a concept representing something that is unbounded or limitless.

When we talk about the limit as x approaches infinity for the exponential function e^x, it means that the function grows without bound as x gets larger and larger. In other words, the value of e^x becomes arbitrarily large as x becomes increasingly large, but it never reaches a specific finite value at infinity.

In calculus and mathematical analysis, the concept of limits and infinite series is used to study and understand functions that behave in certain ways as their inputs approach infinity. As such, e^∞ is used in limits and asymptotic analysis to describe the behavior of exponential functions as their inputs tend towards infinity.