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Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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![### Limit Problem for Educational Website
**Problem Statement:**
In the find and prove of \( \lim_{{x} \to 0} \left( x^3 \right) \), how and what \( \delta \) should be defined in terms of \( \epsilon \)?
**Answer Choices:**
A. \( \delta = \min \left\{ 1, \frac{\epsilon}{3} \right\} \)
B. \( \delta = \epsilon^3 \)
C. \( \delta = \min \left\{ 1, \sqrt[3]{\epsilon} \right\} \)
D. \( \delta = \sqrt[3]{\epsilon} \)
E. NO correct choices
**Options for Selection:**
- ( ) E
- ( ) C
- ( ) A
- ( ) B
- ( ) D
**Explanation:**
This problem involves finding the correct \( \delta \) in terms of \( \epsilon \) to properly define the limit \( \lim_{{x} \to 0} \left( x^3 \right) \). The choices provided suggest different potential relationships between \( \delta \) and \( \epsilon \). Understanding the definition of limits and the epsilon-delta condition is crucial in selecting the correct answer.](https://content.bartleby.com/qna-images/question/2f1709b6-d6cf-4974-9d61-8af289333b8d/2ecdf5ba-e1bd-4ed8-8ef7-d646e2d73475/my4rgv_thumbnail.png)
Transcribed Image Text:### Limit Problem for Educational Website
**Problem Statement:**
In the find and prove of \( \lim_{{x} \to 0} \left( x^3 \right) \), how and what \( \delta \) should be defined in terms of \( \epsilon \)?
**Answer Choices:**
A. \( \delta = \min \left\{ 1, \frac{\epsilon}{3} \right\} \)
B. \( \delta = \epsilon^3 \)
C. \( \delta = \min \left\{ 1, \sqrt[3]{\epsilon} \right\} \)
D. \( \delta = \sqrt[3]{\epsilon} \)
E. NO correct choices
**Options for Selection:**
- ( ) E
- ( ) C
- ( ) A
- ( ) B
- ( ) D
**Explanation:**
This problem involves finding the correct \( \delta \) in terms of \( \epsilon \) to properly define the limit \( \lim_{{x} \to 0} \left( x^3 \right) \). The choices provided suggest different potential relationships between \( \delta \) and \( \epsilon \). Understanding the definition of limits and the epsilon-delta condition is crucial in selecting the correct answer.
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