2. Use the definition of the limit to prove that lim (r+2y – 1) = 1. (1,9)¬(0,1)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Question 2:**

**Use the definition of the limit to prove that \(\lim_{(x,y) \to (0,1)} (x + 2y - 1) = 1\).**

In this problem, you are required to use the formal definition of a limit in multivariable calculus to demonstrate that as \((x,y)\) approaches \((0,1)\), the expression \((x + 2y - 1)\) approaches 1. This exercise reinforces the concept of limits in a two-dimensional space and the significance of precise mathematical proofs in analysis.
Transcribed Image Text:**Question 2:** **Use the definition of the limit to prove that \(\lim_{(x,y) \to (0,1)} (x + 2y - 1) = 1\).** In this problem, you are required to use the formal definition of a limit in multivariable calculus to demonstrate that as \((x,y)\) approaches \((0,1)\), the expression \((x + 2y - 1)\) approaches 1. This exercise reinforces the concept of limits in a two-dimensional space and the significance of precise mathematical proofs in analysis.
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