The expression you have shown is a limit that approaches an important constant in calculus:

$\lim_{x \to \infty} \left( 1 + \frac{1}{x} \right)^x$

This limit is well-known to approach the number e, which is approximately 2.71828. It is a fundamental limit in calculus and represents the base of the natural logarithm.

Explanation:

The limit describes how the expression $\left( 1 + \frac{1}{x} \right)^x$ behaves as $x$ increases indefinitely. As $x$ gets larger, the value of the expression approaches $e$.

Would you like further clarification on this limit or its derivation?

Here are five related questions:

1. What is the mathematical significance of the number $e$?
2. How is the number $e$ used in real-world applications?
3. Can we derive $e$ using series expansions?
4. What are some of the properties of exponential functions?
5. How does this limit relate to the compound interest formula?

Tip: Understanding the limit of this type helps in mastering exponential growth problems, which appear frequently in areas such as finance, biology, and physics.