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The limit of f(x, y) as y → 0 along the path a x=y is 1. The limit of f(x, y) as y → 0 along the path z = y² is 1. • ƒ(0,0) = 2. Which of the following statements must be true?

The limit of f(x, y) as y → 0 along the path a x=y is 1. The limit of f(x, y) as y → 0 along the path z = y² is 1. • ƒ(0,0) = 2. Which of the following statements must be true?

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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Let f(x, y) be a function such that The limit of f(x, y) as y → 0 along the path x = y is 1. . The limit of f(x, y) as y → 0 along the path z = y² is 1. f(0,0) = 2. Which of the following statements must be true? Of is not continuous at (0, 0). O The limit of f(x, y) as y→ 0 along the path = 2y is 1. lim f(x, y) does not exist. (x,y) →(0,0) lim f(x, y) = 1 (x,y) (0,0)
Transcribed Image Text:Let f(x, y) be a function such that The limit of f(x, y) as y → 0 along the path x = y is 1. . The limit of f(x, y) as y → 0 along the path z = y² is 1. f(0,0) = 2. Which of the following statements must be true? Of is not continuous at (0, 0). O The limit of f(x, y) as y→ 0 along the path = 2y is 1. lim f(x, y) does not exist. (x,y) →(0,0) lim f(x, y) = 1 (x,y) (0,0)
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