Determine if the limits lim (x, y)-(0, 0) f(x, y) exist by changing the problem to polar coordinates. Use the fact that r→ 0+ as (x,y) → (0, 0) in your work. There are several different situations that can arise. First, if the limit blows up or depends on 0 as r→ 0+ then the If(r cos(0), r sin(0))| ≤ g(r) for all (r, e) and lim f(x, y) = 0. Evaluate the limit below. (If an answer does not exist, enter DNE.) g(r)= 0, then r-0+ (5x³+4y³) lim (x, y) (0, 0) x² + y² (5x³ + 4y³) lim (x, y) (0, 0) x² + y² = lim (x,y) → (0, 0)
Determine if the limits lim (x, y)-(0, 0) f(x, y) exist by changing the problem to polar coordinates. Use the fact that r→ 0+ as (x,y) → (0, 0) in your work. There are several different situations that can arise. First, if the limit blows up or depends on 0 as r→ 0+ then the If(r cos(0), r sin(0))| ≤ g(r) for all (r, e) and lim f(x, y) = 0. Evaluate the limit below. (If an answer does not exist, enter DNE.) g(r)= 0, then r-0+ (5x³+4y³) lim (x, y) (0, 0) x² + y² (5x³ + 4y³) lim (x, y) (0, 0) x² + y² = lim (x,y) → (0, 0)
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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Transcribed Image Text:Determine if the limits
lim
(x,y) → (0, 0)
exist by changing the problem to polar coordinates. Use the fact that r → 0+ as (x, y) → (0, 0) in your work. There are several different situations that can arise. First, if the limit blows up or depends on 0 as r → 0 then the
If(r cos(0), r sin(0))| ≤ g(r) for all (r, e) and lim
g(r) = 0, then lim f(x, y) = 0. Evaluate the limit below. (If an answer does not exist, enter DNE.)
(x, y) → (0, 0)
+
ro+
lim
(x, y) → (0, 0)
f(x, y)
lim
(x,y) → (0, 0)
(5x³ + 4y³)
(5x³ + 4y³) |
=
+
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