Calculus: Early Transcendentals
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.
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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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