5 lim (1 ! ( 1 + ²) ²³.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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evaluate, if it exists, the following limit
![The image shows the following mathematical expression related to limits and exponents:
\[ \lim_{x \rightarrow \infty} \left(1 + \frac{5}{x}\right)^x \]
This notation is used to describe the behavior of the given expression as \( x \) approaches infinity. It is an example of an exponential limit often encountered in calculus and analysis. Specifically, this is a form of the limit that leads to the exponential function, indicating growth or decay. This particular limit is analogous to the expression that defines the constant \( e \) but with a different coefficient in the fraction. In this case, it provides a form for computing \( e^5 \) when evaluated.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a780900-9b69-4fe9-9f43-185066935266%2Fd531ed25-6425-4b49-9e99-ebe853ec3aaa%2Fklxpa5_processed.png&w=3840&q=75)
Transcribed Image Text:The image shows the following mathematical expression related to limits and exponents:
\[ \lim_{x \rightarrow \infty} \left(1 + \frac{5}{x}\right)^x \]
This notation is used to describe the behavior of the given expression as \( x \) approaches infinity. It is an example of an exponential limit often encountered in calculus and analysis. Specifically, this is a form of the limit that leads to the exponential function, indicating growth or decay. This particular limit is analogous to the expression that defines the constant \( e \) but with a different coefficient in the fraction. In this case, it provides a form for computing \( e^5 \) when evaluated.
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