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1. Match the rule or formula's name with its characteristics by putting the lowercase letter on the line. M(b-a)³ where M = 7 24n² A. Midpoint Rule B. Trapezoidal Rule C. Simpson's Rule D. Error bound for Midpoint Rule E. Error bound for Trapezoidal Rule F. Error bound for Simpson's Rule a. Error < b. Ax (f(xo) + 4f(x1) +2f(x₂)++4f(n-1) + f(n)) 3 M(b- - a)5 c. Error d. Σ. f(mi)Δα i=1 7 180m4 f. Error = max(f"(x)) where M = M(b-a)³ 12n² e. Aª (ƒ (xo) + 2ƒ (x1) + 2ƒ(x2) + ··· + 2ƒ (xn−1) + ƒ (xn)) =max(f"(x)|) max(f(¹4)(x)) where M =

1. Match the rule or formula's name with its characteristics by putting the lowercase letter on the line. M(b-a)³ where M = 7 24n² A. Midpoint Rule B. Trapezoidal Rule C. Simpson's Rule D. Error bound for Midpoint Rule E. Error bound for Trapezoidal Rule F. Error bound for Simpson's Rule a. Error < b. Ax (f(xo) + 4f(x1) +2f(x₂)++4f(n-1) + f(n)) 3 M(b- - a)5 c. Error d. Σ. f(mi)Δα i=1 7 180m4 f. Error = max(f"(x)) where M = M(b-a)³ 12n² e. Aª (ƒ (xo) + 2ƒ (x1) + 2ƒ(x2) + ··· + 2ƒ (xn−1) + ƒ (xn)) =max(f"(x)|) max(f(¹4)(x)) where M =

Calculus: Early Transcendentals
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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# Numerical Integration: Matching Rules and Formulas **Exercise: Match the rule or formula's name with its characteristics by putting the lowercase letter on the line.** ### Rules and Formulas A. **Midpoint Rule** _______ B. **Trapezoidal Rule** _______ C. **Simpson’s Rule** _______ D. **Error bound for Midpoint Rule** _______ E. **Error bound for Trapezoidal Rule** _______ F. **Error bound for Simpson’s Rule** _______ ### Characteristics a. \( \text{Error} \leq \frac{M(b-a)^3}{24n^2}, \quad \text{where} \ M = \max(|f''(x)|) \) b. \( \frac{\Delta x}{3} (f(x_0) + 4f(x_1) + 2f(x_2) + \cdots + 4f(x_{n-1}) + f(x_n)) \) c. \( \text{Error} \leq \frac{M(b-a)^5}{180n^4}, \quad \text{where} \ M = \max(|f^{(4)}(x)|) \) d. \( \sum_{i=1}^{n} f(m_i)\Delta x \) e. \( \frac{\Delta x}{2} (f(x_0) + 2f(x_1) + 2f(x_2) + \cdots + 2f(x_{n-1}) + f(x_n)) \) f. \( \text{Error} \leq \frac{M(b-a)^3}{12n^2}, \quad \text{where} \ M = \max(|f''(x)|) \) **Instructions**: Determine which characteristic corresponds to each rule or error bound by matching the letter of the characteristic with the rule or error bound.
Transcribed Image Text:# Numerical Integration: Matching Rules and Formulas **Exercise: Match the rule or formula's name with its characteristics by putting the lowercase letter on the line.** ### Rules and Formulas A. **Midpoint Rule** _______ B. **Trapezoidal Rule** _______ C. **Simpson’s Rule** _______ D. **Error bound for Midpoint Rule** _______ E. **Error bound for Trapezoidal Rule** _______ F. **Error bound for Simpson’s Rule** _______ ### Characteristics a. \( \text{Error} \leq \frac{M(b-a)^3}{24n^2}, \quad \text{where} \ M = \max(|f''(x)|) \) b. \( \frac{\Delta x}{3} (f(x_0) + 4f(x_1) + 2f(x_2) + \cdots + 4f(x_{n-1}) + f(x_n)) \) c. \( \text{Error} \leq \frac{M(b-a)^5}{180n^4}, \quad \text{where} \ M = \max(|f^{(4)}(x)|) \) d. \( \sum_{i=1}^{n} f(m_i)\Delta x \) e. \( \frac{\Delta x}{2} (f(x_0) + 2f(x_1) + 2f(x_2) + \cdots + 2f(x_{n-1}) + f(x_n)) \) f. \( \text{Error} \leq \frac{M(b-a)^3}{12n^2}, \quad \text{where} \ M = \max(|f''(x)|) \) **Instructions**: Determine which characteristic corresponds to each rule or error bound by matching the letter of the characteristic with the rule or error bound.
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