Examine the behavior of f(r, y) as (z,1) approaches (0,0) along straighe lines chrough the origin. 9z +3y Use "infimity" for "00" and "-infimity" for "-0" Use "DNE" for "Does not exier". (a) Taking a linear approach to the origin along the y-axis, we find Ty lim (z.v) (0,0), z 0 ( 9+3y (b) Taking a linear approach to the origin along the z-axis, we find zy lim (z.v) (0,0), y 0 9z2 +3y () Taking a linear approach to the origin along a Ine mE with m70 we hnd lim lim (z.v) (0,0), y mz 9z +3y 10 we hnd (d) T.king a linear approach to dhe origin along the line y lim (ry) (00). v 9e 3y 10z
Examine the behavior of f(r, y) as (z,1) approaches (0,0) along straighe lines chrough the origin. 9z +3y Use "infimity" for "00" and "-infimity" for "-0" Use "DNE" for "Does not exier". (a) Taking a linear approach to the origin along the y-axis, we find Ty lim (z.v) (0,0), z 0 ( 9+3y (b) Taking a linear approach to the origin along the z-axis, we find zy lim (z.v) (0,0), y 0 9z2 +3y () Taking a linear approach to the origin along a Ine mE with m70 we hnd lim lim (z.v) (0,0), y mz 9z +3y 10 we hnd (d) T.king a linear approach to dhe origin along the line y lim (ry) (00). v 9e 3y 10z
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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Please look at the question and answer correctly for c and d parts only... Needed correct answers..
Transcribed Image Text:You have answered 4 out of 6 parts correctily.
Examine the behavior of f(r,y)
as (z, 1) approaches (0,0) along straighe lines through the origin.
9z +3y
Use "infimity" for "00" and"infinity Jor -o0 Use DNE" for "Does not exist"
(a) Taking a linear approach to the origin along the y-axis, we find
lim
(Z.v) (0,0), 0 9+ 3
(b) Taking a linear approach to the origin along the z-axis, we find
lim
(29) >(0,0), y 0922+3y
(c) Taking a linear approach to the origin alonga line y ma wirh m/0 we fnd
lim
lim
(cv) (0,0), y mz
92 +3y
(d) Taking a lnear approach te the erign along the hine y-10r we ht
zy
Tim
10z
PILOM
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