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For Exercises 1 and 2, let f(x, y) = x +2y on R:0< x < 2. 0

For Exercises 1 and 2, let f(x, y) = x +2y on R:0< x < 2. 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I need help with #2. Thank you.
**For Exercises 1 and 2, let** \[ f(x, y) = x + 2y \quad \text{on} \quad R: 0 \leq x \leq 2, \quad 0 \leq y \leq 1. \] **and let P be the partition** \( P = P_1 \times P_2 \). 1. **Find** \( L_f(P) \) **and** \( U_f(P) \) **given that** \( P_1 = \{0, 1, \frac{3}{2}, 2\} \) **and** \( P_2 = \{0, \frac{1}{2}, 1\} \). 2. **Find** \( L_f(P) \) **and** \( U_f(P) \) **given that** \( P_1 = \{0, \frac{1}{2}, 1, \frac{3}{2}, 2\} \) **and** \( P_2 = \{0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1\} \).
Transcribed Image Text:**For Exercises 1 and 2, let** \[ f(x, y) = x + 2y \quad \text{on} \quad R: 0 \leq x \leq 2, \quad 0 \leq y \leq 1. \] **and let P be the partition** \( P = P_1 \times P_2 \). 1. **Find** \( L_f(P) \) **and** \( U_f(P) \) **given that** \( P_1 = \{0, 1, \frac{3}{2}, 2\} \) **and** \( P_2 = \{0, \frac{1}{2}, 1\} \). 2. **Find** \( L_f(P) \) **and** \( U_f(P) \) **given that** \( P_1 = \{0, \frac{1}{2}, 1, \frac{3}{2}, 2\} \) **and** \( P_2 = \{0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1\} \).
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