Evaluate the limit. Note: Enter oo (two 'o's) for infinity, . 1 1 Viel In(t-1) lim t→∞ Check Answer
Evaluate the limit. Note: Enter oo (two 'o's) for infinity, . 1 1 Viel In(t-1) lim t→∞ Check Answer
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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![**Question 6**
Evaluate the limit. Note: Enter oo (two 'o's) for infinity, ∞.
\[
\lim_{{t \to \infty}} \left\langle \frac{1}{\sqrt{t}}, e^{1-t}, \frac{1}{\ln(t-1)} \right\rangle = \_\_\_
\]
**[Check Answer]**
This problem requires calculating the limit of a vector as \( t \) approaches infinity, where the vector components are \(\frac{1}{\sqrt{t}}\), \(e^{1-t}\), and \(\frac{1}{\ln(t-1)}\). The goal is to determine the behavior of each component independently as \( t \) tends toward infinity, then provide the overall limit of the vector based on these results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a3f3121-07ef-4e2d-8122-d3ccd0e5a601%2Ff43af326-dd38-4533-b1c7-61030dea4240%2Fb4b289t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 6**
Evaluate the limit. Note: Enter oo (two 'o's) for infinity, ∞.
\[
\lim_{{t \to \infty}} \left\langle \frac{1}{\sqrt{t}}, e^{1-t}, \frac{1}{\ln(t-1)} \right\rangle = \_\_\_
\]
**[Check Answer]**
This problem requires calculating the limit of a vector as \( t \) approaches infinity, where the vector components are \(\frac{1}{\sqrt{t}}\), \(e^{1-t}\), and \(\frac{1}{\ln(t-1)}\). The goal is to determine the behavior of each component independently as \( t \) tends toward infinity, then provide the overall limit of the vector based on these results.
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