Let ƒ : R² → R and suppose that lim f (x, y) = -10. (x,y)→(3,0) What can you say about the value ƒ (3,0)? Nothing can be said about the value ƒ (3, 0). ƒ (3,0) = -10 f(3,0) = -10 f may or may not be continuous at (3, 0). f is continuous at (3, 0).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let f: R²R and suppose that
lim_ f (x, y) = -10.
(x,y)→(3,0)*
What can you say about the value f (3, 0)?
Nothing can be said about the value ƒ (3, 0).
f(3,0) = -10
ƒ (3,0) = -10
f may or may not be continuous at (3, 0).
f is continuous at (3, 0).
Transcribed Image Text:Let f: R²R and suppose that lim_ f (x, y) = -10. (x,y)→(3,0)* What can you say about the value f (3, 0)? Nothing can be said about the value ƒ (3, 0). f(3,0) = -10 ƒ (3,0) = -10 f may or may not be continuous at (3, 0). f is continuous at (3, 0).
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