This function is given by (a) Find a formula for the single variable function f(0, y). f(0, y) = What is f(0, 0) for this function? f(0,0) Find its limit as y → 0: lim f(0, y) y+0 (b) Based on your work in (a), is the single variable function f(0, y) continuous?? (c) Next, similarly consider f(x, 0). f(x,0) = f(0,0) = lim f(x, 0) 2-0 5xy 2²+y2 (x, y) = (0,0) (x, y) = (0,0). f (2, 3) = { 3²

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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Consider the function f whose graph is shown below.
This function is given by
(a) Find a formula for the single variable function f(0, y).
f(0, y)
What is f(0, 0) for this function?
f(0,0) =
Find its limit as y → 0:
lim f(0, y)
y→0
= {2²²
f(0,0) =
lim f(x, 0)
x-0
f(x, y)
(b) Based on your work in (a), is the single variable function f(0, y) continuous? ?
(c) Next, similarly consider f(x, 0).
f(x,0) =
x²+y², (x, y) = (0,0)
(x, y) = (0,0).
v
Transcribed Image Text:Consider the function f whose graph is shown below. This function is given by (a) Find a formula for the single variable function f(0, y). f(0, y) What is f(0, 0) for this function? f(0,0) = Find its limit as y → 0: lim f(0, y) y→0 = {2²² f(0,0) = lim f(x, 0) x-0 f(x, y) (b) Based on your work in (a), is the single variable function f(0, y) continuous? ? (c) Next, similarly consider f(x, 0). f(x,0) = x²+y², (x, y) = (0,0) (x, y) = (0,0). v
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