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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![Certainly! Below is the transcription appropriate for an educational website with the explanation of the summation notation:
---
### Find the value of the sum
\[ \sum_{i=1}^{4} X_i \]
if \( X_1 = 8 \), \( X_2 = -3 \), \( X_3 = 4 \), \( X_4 = -1 \).
Calculate the value of the sum by substituting the given values of \( X_i \) into the summation.
### Solution:
1. **Summation notation**: The expression \( \sum_{i=1}^{4} X_i \) denotes the sum of the terms \( X_1 \) through \( X_4 \).
2. **Given values**:
- \( X_1 = 8 \)
- \( X_2 = -3 \)
- \( X_3 = 4 \)
- \( X_4 = -1 \)
3. **Substitute and sum**:
\[
\sum_{i=1}^{4} X_i = X_1 + X_2 + X_3 + X_4 = 8 + (-3) + 4 + (-1)
\]
4. **Calculate**:
\[
8 - 3 + 4 - 1 = 8 - 3 = 5
\]
\[
5 + 4 = 9
\]
\[
9 - 1 = 8
\]
Hence, the value of the sum is \( 8 \).
---
Feel free to add illustrative graphs or diagrams to this explanation to further enhance understanding. If you have any questions or need further clarification, please don't hesitate to ask!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2c89fb8-28c7-4f54-82f8-eda7977d51b8%2F2b742c4f-f279-4b0e-ab94-71d14219ed34%2Fubspg0u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Below is the transcription appropriate for an educational website with the explanation of the summation notation:
---
### Find the value of the sum
\[ \sum_{i=1}^{4} X_i \]
if \( X_1 = 8 \), \( X_2 = -3 \), \( X_3 = 4 \), \( X_4 = -1 \).
Calculate the value of the sum by substituting the given values of \( X_i \) into the summation.
### Solution:
1. **Summation notation**: The expression \( \sum_{i=1}^{4} X_i \) denotes the sum of the terms \( X_1 \) through \( X_4 \).
2. **Given values**:
- \( X_1 = 8 \)
- \( X_2 = -3 \)
- \( X_3 = 4 \)
- \( X_4 = -1 \)
3. **Substitute and sum**:
\[
\sum_{i=1}^{4} X_i = X_1 + X_2 + X_3 + X_4 = 8 + (-3) + 4 + (-1)
\]
4. **Calculate**:
\[
8 - 3 + 4 - 1 = 8 - 3 = 5
\]
\[
5 + 4 = 9
\]
\[
9 - 1 = 8
\]
Hence, the value of the sum is \( 8 \).
---
Feel free to add illustrative graphs or diagrams to this explanation to further enhance understanding. If you have any questions or need further clarification, please don't hesitate to ask!
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