The expression e to the power of infinity refers to the mathematical limit as the exponent grows without bound. In simpler terms, we are looking at the behavior of e^x as x approaches infinity.
Since e is approximately 2.71828, we know it is greater than 1. When we raise a number greater than 1 to a power that increases without limit, the result also increases without limit. Therefore, as x becomes infinitely large, e^x approaches infinity.
Thus, we conclude that:
- e to the power of infinity = ∞
This concept is fundamental in calculus and helps in understanding exponential growth and its implications in various fields such as finance, biology, and physics.