d) Let the function: f(x, y) = 3, < 0, Find the following limits: (i), lim (z.y)-(3,-2) f(x, y) , (ii) lim (2.y)(-2,1) f(2, y) (i), lim (2,-y)→(0,0) f(z, y)
d) Let the function: f(x, y) = 3, < 0, Find the following limits: (i), lim (z.y)-(3,-2) f(x, y) , (ii) lim (2.y)(-2,1) f(2, y) (i), lim (2,-y)→(0,0) f(z, y)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![d) Let the function:
f(x, y) =
|, X< 0,
Find the following limits:
(i)
f (x, y) , (ii)
lim
(2,-y)→(0,0)
f(z, y)
(z,y)-(3,-2)
lim
lim
(x,y)→(-2,1)
f(z, y) (iii),
e) What does it mean to say that a function f(x, y) is continuous at a point (To, Yo)? State at
least 3 facts.
f) Show that fa(0,0) and fy (0,0) exist, but f is not differentiable at the point (0,0):
S, (7, y) # (0, 0)
(x, y) = (0,0)
J0, z <y< 2?
1, otherwise
(ii) f(x,y) =
(i) f(x, y) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95ae200a-d89c-4ac7-875f-557991089bc2%2F07f77fa7-40d8-48ea-8b90-dcd87dd47a79%2Fm4g9nu4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:d) Let the function:
f(x, y) =
|, X< 0,
Find the following limits:
(i)
f (x, y) , (ii)
lim
(2,-y)→(0,0)
f(z, y)
(z,y)-(3,-2)
lim
lim
(x,y)→(-2,1)
f(z, y) (iii),
e) What does it mean to say that a function f(x, y) is continuous at a point (To, Yo)? State at
least 3 facts.
f) Show that fa(0,0) and fy (0,0) exist, but f is not differentiable at the point (0,0):
S, (7, y) # (0, 0)
(x, y) = (0,0)
J0, z <y< 2?
1, otherwise
(ii) f(x,y) =
(i) f(x, y) =
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