9 h(q) 1 1.5 2 2.5 233 667 1906 82 3 5446 Estimate h' (2) using the table above. Use points on either side of the given point for your estimate. Round to 3 decimal places if necessary. h' (2) ~
9 h(q) 1 1.5 2 2.5 233 667 1906 82 3 5446 Estimate h' (2) using the table above. Use points on either side of the given point for your estimate. Round to 3 decimal places if necessary. h' (2) ~
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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![On this educational website, students are presented with a table and a task aimed at estimating the derivative of a function at a specific point using given discrete data. The table and task details are outlined below:
---
### Table:
| \( q \) | 1 | 1.5 | 2 | 2.5 | 3 |
|----|----|-----|-----|-----|-----|
| \( h(q) \) | 82 | 233 | 667 | 1906 | 5446 |
#### Instructions:
Estimate \( h'(2) \) using the table above. Use points on either side of the given point for your estimate. Round to 3 decimal places if necessary.
**Solution box:**
\[ h'(2) \approx \]
\[ \_\_\_\_\_\_\_\_\_\_ \]
Graph Details:
- The table presented shows the values of \( q \) and their corresponding \( h(q) \).
#### Estimation Process:
To estimate the derivative \( h'(2) \), which represents the rate of change of \( h(q) \) at \( q = 2 \), students should use the central difference method. This method provides a more accurate estimate by considering the values on either side of the point of interest:
\[ h'(2) \approx \frac{h(2.5) - h(1.5)}{2.5 - 1.5} \]
Substituting the values from the table:
\[ h'(2) \approx \frac{1906 - 233}{2.5 - 1.5} \]
\[ h'(2) \approx \frac{1673}{1} \]
\[ h'(2) \approx 1673 \]
So, the estimated value is:
\[ h'(2) \approx 1673 \]
---
This step-by-step explanation helps students understand how to use the given data in the table to estimate the derivative of a function at a specific point using numerical methods.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78020af4-edac-45d4-a6db-c9f21dc2273f%2Fd1729a3d-f926-4318-96e5-0b73c30ce3aa%2Fangdeyi_processed.png&w=3840&q=75)
Transcribed Image Text:On this educational website, students are presented with a table and a task aimed at estimating the derivative of a function at a specific point using given discrete data. The table and task details are outlined below:
---
### Table:
| \( q \) | 1 | 1.5 | 2 | 2.5 | 3 |
|----|----|-----|-----|-----|-----|
| \( h(q) \) | 82 | 233 | 667 | 1906 | 5446 |
#### Instructions:
Estimate \( h'(2) \) using the table above. Use points on either side of the given point for your estimate. Round to 3 decimal places if necessary.
**Solution box:**
\[ h'(2) \approx \]
\[ \_\_\_\_\_\_\_\_\_\_ \]
Graph Details:
- The table presented shows the values of \( q \) and their corresponding \( h(q) \).
#### Estimation Process:
To estimate the derivative \( h'(2) \), which represents the rate of change of \( h(q) \) at \( q = 2 \), students should use the central difference method. This method provides a more accurate estimate by considering the values on either side of the point of interest:
\[ h'(2) \approx \frac{h(2.5) - h(1.5)}{2.5 - 1.5} \]
Substituting the values from the table:
\[ h'(2) \approx \frac{1906 - 233}{2.5 - 1.5} \]
\[ h'(2) \approx \frac{1673}{1} \]
\[ h'(2) \approx 1673 \]
So, the estimated value is:
\[ h'(2) \approx 1673 \]
---
This step-by-step explanation helps students understand how to use the given data in the table to estimate the derivative of a function at a specific point using numerical methods.
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