Question 1 A function of two variables (x, y) is given as: (a) (b) (c) f(x, y) = = x³ +y³ x³+y³ +1-1 Determine the existence of lim f(x, y). If exist, evaluate it. (x,y)-(1,1) Determine the existence of lim f(x,y). If exist, evaluate it. If there is a definition at point (0,0), f(x, y) = m. Find the value of m to make the function f(x, y) is continuous at point (0,0).

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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Question 1
A function of two variables (x, y) is given as:
(a)
(b)
f(x, y) =
x² + y²
x³+y³ +1-1
Determine the existence of lim f(x, y). If exist, evaluate it.
(x,y)-(1,1)
Determine the existence of lim f(x, y). If exist, evaluate it.
(c)
If there is a definition at point (0,0), f(x, y) = m. Find the value of m to make
the function f(x, y) is continuous at point (0,0).
Transcribed Image Text:Question 1 A function of two variables (x, y) is given as: (a) (b) f(x, y) = x² + y² x³+y³ +1-1 Determine the existence of lim f(x, y). If exist, evaluate it. (x,y)-(1,1) Determine the existence of lim f(x, y). If exist, evaluate it. (c) If there is a definition at point (0,0), f(x, y) = m. Find the value of m to make the function f(x, y) is continuous at point (0,0).
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