Find the following limit: limit as x approaches infinity of (1 + 1/x)^x.

Question:

Find the following limit: {eq}\lim_{x\rightarrow \, \infty} \, (1 + \frac{1}{x})^x {/eq}.

The Limit in Calculus:

The concept of the limit is one of the fundamental ideas used in calculus.

The limit of a function is used to analyze the behavior of a function near the input point as well as define a derivative's continuity and integrals.

To solve this problem, we'll use the common limit: {eq}\lim_{x\rightarrow \, \infty} \, (1 + \frac{k}{x})^x = e^k {/eq}

Answer and Explanation:

We are given:

{eq}\lim_{x\rightarrow \, \infty} \, (1 + \frac{1}{x})^x {/eq}

Apply the common limit: {eq}\lim_{x\rightarrow \, \infty} \, (1 +...

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Understanding the Properties of Limits

from Math 104: Calculus

Chapter 5 / Lesson 5
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