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A day full of math games & activities. Find one near you.

A day full of math games & activities. Find one near you.

A day full of math games & activities. Find one near you.

# 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 ∞.

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