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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Question
How would you solve problem 42?
![**Graphs and Diagrams Description:**
The page contains two graphs on the top.
1. **First Graph:**
- The graph represents the function \(y = x^3 - 3x\).
- The x-axis and y-axis are marked with intervals ranging from -2 to 2.
- The curve crosses the x-axis at three points, approximately \((-2, 0)\), \((0, 0)\), and \((2, 0)\).
- The graph shows a typical cubic shape, with one local maximum and one local minimum.
- The area between the curve and the x-axis is highlighted in orange.
2. **Second Graph:**
- The graph represents the function \(y = -2e^{3x}\).
- The x-axis ranges from negative to positive values, while the y-axis shows values near -2.
- This graph shows an exponential decay as \(x\) increases, starting from negative infinity on the y-axis.
- The area under the curve is shaded in orange.
**Homework/Practice Problems:**
Evaluate the following integrals:
39. \(\int_{1}^{3} (3t^2 + 7) \, dt\)
40. \(\int_{1}^{2} (4t^3 - 1) \, dt\)
41. \(\int_{1}^{4} (\sqrt{x - 1}) \, dx\)
42. \(\int_{1}^{8} (\sqrt[3]{x - 2}) \, dx\)
43. \(\int_{-2}^{5} (2x^2 - 3x + 7) \, dx\)
44. \(\int_{-2}^{3} (-x^2 + 4x - 5) \, dx\)
45. \(\int_{-5}^{2} e^{t} \, dt\)
46. \(\int_{-2}^{3} e^{-t} \, dt\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F631ebc5c-4ef7-493e-ad4a-59361e0347ad%2Fe8e0a4ff-64f7-4f61-ae0a-951ae53b2c20%2Fu7i640l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graphs and Diagrams Description:**
The page contains two graphs on the top.
1. **First Graph:**
- The graph represents the function \(y = x^3 - 3x\).
- The x-axis and y-axis are marked with intervals ranging from -2 to 2.
- The curve crosses the x-axis at three points, approximately \((-2, 0)\), \((0, 0)\), and \((2, 0)\).
- The graph shows a typical cubic shape, with one local maximum and one local minimum.
- The area between the curve and the x-axis is highlighted in orange.
2. **Second Graph:**
- The graph represents the function \(y = -2e^{3x}\).
- The x-axis ranges from negative to positive values, while the y-axis shows values near -2.
- This graph shows an exponential decay as \(x\) increases, starting from negative infinity on the y-axis.
- The area under the curve is shaded in orange.
**Homework/Practice Problems:**
Evaluate the following integrals:
39. \(\int_{1}^{3} (3t^2 + 7) \, dt\)
40. \(\int_{1}^{2} (4t^3 - 1) \, dt\)
41. \(\int_{1}^{4} (\sqrt{x - 1}) \, dx\)
42. \(\int_{1}^{8} (\sqrt[3]{x - 2}) \, dx\)
43. \(\int_{-2}^{5} (2x^2 - 3x + 7) \, dx\)
44. \(\int_{-2}^{3} (-x^2 + 4x - 5) \, dx\)
45. \(\int_{-5}^{2} e^{t} \, dt\)
46. \(\int_{-2}^{3} e^{-t} \, dt\)
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