Find the limit: -3t e to - 1 t10 – t9' 2+ t -5 lim( t t→0
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
![Find the limit:
\[
\lim_{{t \to 0}} \left\langle \frac{{e^{-3t} - 1}}{t}, \frac{{t^9}}{{t^{10} - t^9}}, \frac{{-5}}{{2 + t}} \right\rangle
\]
This image presents a mathematical expression involving the limit of a vector function as \( t \) approaches 0. The vector has three components:
1. \(\frac{{e^{-3t} - 1}}{t}\)
2. \(\frac{{t^9}}{{t^{10} - t^9}}\)
3. \(\frac{{-5}}{{2 + t}}\)
Each component of the vector requires evaluating the limit as \( t \) approaches 0. The expressions in each component need to be simplified or evaluated to find the limit values accordingly.
The diagram illustrates spaces indicating where the results should be entered, suggesting a solution process for each component of the vector separately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc247148b-ac88-4d23-ab16-d846cf9acaa7%2Fde616626-b204-4e0f-bbbc-a3c7b02e05dd%2Fvopqt6_processed.png&w=3840&q=75)
Transcribed Image Text:Find the limit:
\[
\lim_{{t \to 0}} \left\langle \frac{{e^{-3t} - 1}}{t}, \frac{{t^9}}{{t^{10} - t^9}}, \frac{{-5}}{{2 + t}} \right\rangle
\]
This image presents a mathematical expression involving the limit of a vector function as \( t \) approaches 0. The vector has three components:
1. \(\frac{{e^{-3t} - 1}}{t}\)
2. \(\frac{{t^9}}{{t^{10} - t^9}}\)
3. \(\frac{{-5}}{{2 + t}}\)
Each component of the vector requires evaluating the limit as \( t \) approaches 0. The expressions in each component need to be simplified or evaluated to find the limit values accordingly.
The diagram illustrates spaces indicating where the results should be entered, suggesting a solution process for each component of the vector separately.
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