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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![The image contains a mathematical expression for solving a definite integral:
\[
56. \int_{-1}^{2} \frac{4}{x^3} \, dx = \left[ -\frac{2}{x^2} \right]_{-1}^{2} = -\frac{3}{2}
\]
1. **Definite Integral**: The integral from \(-1\) to \(2\) of \(\frac{4}{x^3}\, dx\).
2. **Antiderivative**: The antiderivative of \(\frac{4}{x^3}\) is \(-\frac{2}{x^2}\).
3. **Evaluation of Bounds**: The antiderivative is evaluated from \(-1\) to \(2\).
4. **Result**: The resulting value of the definite integral is \(-\frac{3}{2}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90d2137b-83f2-4c15-8300-1a033b76054d%2F5345b19d-fd5d-4aaf-9654-01d132291916%2Fxlzvxee_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains a mathematical expression for solving a definite integral:
\[
56. \int_{-1}^{2} \frac{4}{x^3} \, dx = \left[ -\frac{2}{x^2} \right]_{-1}^{2} = -\frac{3}{2}
\]
1. **Definite Integral**: The integral from \(-1\) to \(2\) of \(\frac{4}{x^3}\, dx\).
2. **Antiderivative**: The antiderivative of \(\frac{4}{x^3}\) is \(-\frac{2}{x^2}\).
3. **Evaluation of Bounds**: The antiderivative is evaluated from \(-1\) to \(2\).
4. **Result**: The resulting value of the definite integral is \(-\frac{3}{2}\).
Transcribed Image Text:**55–58. What is wrong with the equation?**
This section invites readers to evaluate given equations and identify any errors present. It encourages critical thinking and problem-solving skills by asking, "What is wrong with the equation?" The purpose is to help learners understand common mistakes and improve their mathematical accuracy.
### Detailed Explanation:
- **Purpose:** The task is designed to enhance analytical skills in equation handling and to foster a deeper understanding of mathematical concepts.
- **Approach:** Students are urged to closely examine each equation, checking for mistakes in operations, balance, or other mathematical rules.
- **Benefit:** By identifying errors, learners gain proficiency in correcting and understanding the rationale behind proper equation formulation.
This exercise is useful for students looking to refine their skills in mathematics and for educators seeking to challenge their students with practical examples.
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