Create a table of value (use 8 values- 4 on the left and 4 on the right) and a calculator to the estimate the limit if it exist. Round off all values to 4 decimals places. ✓lim √10-x-4 21-6 X+6
Create a table of value (use 8 values- 4 on the left and 4 on the right) and a calculator to the estimate the limit if it exist. Round off all values to 4 decimals places. ✓lim √10-x-4 21-6 X+6
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Calculating Limits Using a Table of Values
**Instruction:**
Create a table of values (use 8 values - 4 on the left and 4 on the right) and a calculator to estimate the limit if it exists. Round off all values to 4 decimal places.
\[ \lim_{x \to 6} \frac{\sqrt{10 - x} - 4}{x + 6} \]
---
#### Follow These Steps:
1. **Select Values Around 6:** Choose values for \( x \) that are close to 6, both smaller and larger. For example, values might be 5.9, 5.99, 5.999, 5.9999 (to the left of 6) and 6.1, 6.01, 6.001, 6.0001 (to the right of 6).
2. **Calculate the Function Values:** Use the chosen values of \( x \) to evaluate the function \( \frac{\sqrt{10 - x} - 4}{x + 6} \).
3. **Create the Table:** Document the calculated values in a table format, rounded to 4 decimal places.
---
#### Sample Table:
| \( x \) | \( \frac{\sqrt{10 - x} - 4}{x + 6} \) |
|--------------|--------------------------------------------------|
| 5.9 | Value1 |
| 5.99 | Value2 |
| 5.999 | Value3 |
| 5.9999 | Value4 |
| 6.0001 | Value5 |
| 6.001 | Value6 |
| 6.01 | Value7 |
| 6.1 | Value8 |
(The values Value1, Value2, ..., Value8 should be computed using a calculator, based on the equation provided.)
---
#### Using the Table to Estimate the Limit:
- **Observe the Trend:** Look at the values in the table as \( x \) approaches 6 from both sides.
- **Estimate the Limit:** Based on these values, predict the limit if it appears to converge to a single number.
---
By following these detailed steps, you can effectively estimate the limit for the given function as \( x \) approaches 6. Make sure to carefully compute and round off your](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb62ce946-c165-4529-a471-ed49759bc0da%2F1588edac-52a0-422f-aeda-3a18d57ca3a2%2Flfw5d8x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Calculating Limits Using a Table of Values
**Instruction:**
Create a table of values (use 8 values - 4 on the left and 4 on the right) and a calculator to estimate the limit if it exists. Round off all values to 4 decimal places.
\[ \lim_{x \to 6} \frac{\sqrt{10 - x} - 4}{x + 6} \]
---
#### Follow These Steps:
1. **Select Values Around 6:** Choose values for \( x \) that are close to 6, both smaller and larger. For example, values might be 5.9, 5.99, 5.999, 5.9999 (to the left of 6) and 6.1, 6.01, 6.001, 6.0001 (to the right of 6).
2. **Calculate the Function Values:** Use the chosen values of \( x \) to evaluate the function \( \frac{\sqrt{10 - x} - 4}{x + 6} \).
3. **Create the Table:** Document the calculated values in a table format, rounded to 4 decimal places.
---
#### Sample Table:
| \( x \) | \( \frac{\sqrt{10 - x} - 4}{x + 6} \) |
|--------------|--------------------------------------------------|
| 5.9 | Value1 |
| 5.99 | Value2 |
| 5.999 | Value3 |
| 5.9999 | Value4 |
| 6.0001 | Value5 |
| 6.001 | Value6 |
| 6.01 | Value7 |
| 6.1 | Value8 |
(The values Value1, Value2, ..., Value8 should be computed using a calculator, based on the equation provided.)
---
#### Using the Table to Estimate the Limit:
- **Observe the Trend:** Look at the values in the table as \( x \) approaches 6 from both sides.
- **Estimate the Limit:** Based on these values, predict the limit if it appears to converge to a single number.
---
By following these detailed steps, you can effectively estimate the limit for the given function as \( x \) approaches 6. Make sure to carefully compute and round off your
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