What is e to the power of infinity?

The number 'e' is known as Euler's number, which has a value of approximately 2.71828 and is an irrational number. It has many applications and is used as the base of the natural logarithm.

Answer: e to the power of infinity is infinity (∞).

Let's understand the solution in detail.

Explanation:

We first, look at the graph of y = e^x.

From the graph, we notice that e^x is unbounded in the positive x-axis region.

Hence, e^x tends to approach infinity when x→∞.

Therefore, e to the power of infinity is infinity (∞).

☛Alternate Way of Thinking: e^∞ means e × e × e × .... (infinite number of times). We have e = 2.71828 > 1. When we multiply this number by itself an infinite number of times, we can't even imagine how big a number we will obtain and hence e to the power of infinity results in ∞.