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
![**Instructions:**
Complete the following steps for the given function, interval, and value of \( n \).
**a.** Sketch the graph of the function on the given interval.
**b.** Calculate \(\Delta x\) and the grid points \(x_0, x_1, \ldots, x_n\).
**c.** Illustrate the midpoint Riemann sum by sketching the appropriate rectangles.
**d.** Calculate the midpoint Riemann sum.
Given:
\( f(x) = 2x + 3 \) on \([0,4]; n = 4 \)
---
**a.** Sketch the graph of \( f(x) = 2x + 3 \) on the interval \([0,4]\). Choose the correct graph below.
- **Option A:** Shows a linear graph starting at \( (0, 3) \) with a positive slope, extending to \(x = 8\).
- **Option B:** Shows a curve starting at the origin and sharply increasing past \(y = 150\) as \(x\) increases to 8.
**Graph Analysis:**
- The correct graph for \( f(x) = 2x + 3 \) is a straight line with a slope of 2 and a y-intercept of 3. Option A represents this linear function correctly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffef37ab4-92ab-41e4-8960-935917e1958c%2F326e1639-816f-41e3-a07d-f4f0c018e43a%2Faeys26o_processed.png&w=3840&q=75)
Transcribed Image Text:**Instructions:**
Complete the following steps for the given function, interval, and value of \( n \).
**a.** Sketch the graph of the function on the given interval.
**b.** Calculate \(\Delta x\) and the grid points \(x_0, x_1, \ldots, x_n\).
**c.** Illustrate the midpoint Riemann sum by sketching the appropriate rectangles.
**d.** Calculate the midpoint Riemann sum.
Given:
\( f(x) = 2x + 3 \) on \([0,4]; n = 4 \)
---
**a.** Sketch the graph of \( f(x) = 2x + 3 \) on the interval \([0,4]\). Choose the correct graph below.
- **Option A:** Shows a linear graph starting at \( (0, 3) \) with a positive slope, extending to \(x = 8\).
- **Option B:** Shows a curve starting at the origin and sharply increasing past \(y = 150\) as \(x\) increases to 8.
**Graph Analysis:**
- The correct graph for \( f(x) = 2x + 3 \) is a straight line with a slope of 2 and a y-intercept of 3. Option A represents this linear function correctly.
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