Consider the following. lim X-0 Create a table of values for the function. (Round your answers to four decimal places.) X f(x) -0.1 lim X-0 sin(2x) X sin(2x) X Need Help? -0.01 Read It -0.001 Use the table to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answer to four decimal places.) 0.001 0.01 0.1
Consider the following. lim X-0 Create a table of values for the function. (Round your answers to four decimal places.) X f(x) -0.1 lim X-0 sin(2x) X sin(2x) X Need Help? -0.01 Read It -0.001 Use the table to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answer to four decimal places.) 0.001 0.01 0.1
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
![**Understanding Limits in Calculus**
**Consider the following limit problem:**
\[
\lim_{{x \to 0}} \frac{{\sin(2x)}}{x}
\]
**Create a Table of Values for the Function:**
To estimate the limit, create a table of values. Round your answers to four decimal places.
| \( x \) | \(-0.1\) | \(-0.01\) | \(-0.001\) | \(0.001\) | \(0.01\) | \(0.1\) |
|----------|----------|-----------|------------|-----------|----------|---------|
| \( f(x) \) | | | | | | |
**Estimation and Graphical Confirmation:**
1. Use the table to estimate the limit.
2. Use a graphing utility to graph the function and confirm your result.
3. Round your answer to four decimal places.
\[
\lim_{{x \to 0}} \frac{{\sin(2x)}}{x} \approx \_\_\_
\]
**Additional Resources:**
Need help? Click the "Read It" button for more information and guidance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93c649eb-38c5-4eac-87a7-63d0d31ecd5d%2Fcf6c5624-a39a-438a-b139-10e93672fb9b%2Fdt2l3sn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Limits in Calculus**
**Consider the following limit problem:**
\[
\lim_{{x \to 0}} \frac{{\sin(2x)}}{x}
\]
**Create a Table of Values for the Function:**
To estimate the limit, create a table of values. Round your answers to four decimal places.
| \( x \) | \(-0.1\) | \(-0.01\) | \(-0.001\) | \(0.001\) | \(0.01\) | \(0.1\) |
|----------|----------|-----------|------------|-----------|----------|---------|
| \( f(x) \) | | | | | | |
**Estimation and Graphical Confirmation:**
1. Use the table to estimate the limit.
2. Use a graphing utility to graph the function and confirm your result.
3. Round your answer to four decimal places.
\[
\lim_{{x \to 0}} \frac{{\sin(2x)}}{x} \approx \_\_\_
\]
**Additional Resources:**
Need help? Click the "Read It" button for more information and guidance.
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