lim In(|x|— 1) (cos(x))* Oo O DNE O 00
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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Having trouble with the right and left side limits. What formula do you do?
![The expression shown is a limit problem:
\[
\lim_{{x \to +\infty}} \frac{{\ln(|x| - 1)}}{{(\cos(x))^x}}
\]
The task is to evaluate this limit as \( x \) approaches positive infinity. The possible answer choices provided are:
- \(0\)
- DNE (Does Not Exist)
- \( -\infty \)
- \( \infty \)
This requires analyzing the behavior of both the numerator and denominator as \( x \) grows indefinitely. The result will indicate whether the expression converges to a particular value or diverges.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc388c4d9-a82e-4d00-b1c6-bf9fe1b7875d%2Faaea1d4d-560c-41d9-921b-5e2b9024df1b%2F0yinusc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The expression shown is a limit problem:
\[
\lim_{{x \to +\infty}} \frac{{\ln(|x| - 1)}}{{(\cos(x))^x}}
\]
The task is to evaluate this limit as \( x \) approaches positive infinity. The possible answer choices provided are:
- \(0\)
- DNE (Does Not Exist)
- \( -\infty \)
- \( \infty \)
This requires analyzing the behavior of both the numerator and denominator as \( x \) grows indefinitely. The result will indicate whether the expression converges to a particular value or diverges.
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