Compute the following limit along lines of the form y = mx, for m 0, and along the parabola y = x. What can you conclude? 15ху lim (x,y)-(0,0) x° + yx Along the line y = mx, the limit lim f(x, y) =|. Along the parabola y =x, the limit (х, у) — (0, 0) f(x, y) (х, у) — (0, 0) lim f(x, y) =. Therefore lim (x, y)→(0, 0)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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Compute the following limit along lines of the form y = mx, for m 0, and along the parabola y = x. What can
you conclude?
15ху
lim
(х.у)—(0,0) х° + ух
.....
Along the line y = mx, the limit
lim
f(x, y) =|
. Along the parabola y = x, the limit
(x, y)→(0, 0)
lim
f(x, y) = |. Therefore
lim
f(x, у)
(х, у) — (0, 0)
(х, у) — (0, 0)
Transcribed Image Text:2 Compute the following limit along lines of the form y = mx, for m 0, and along the parabola y = x. What can you conclude? 15ху lim (х.у)—(0,0) х° + ух ..... Along the line y = mx, the limit lim f(x, y) =| . Along the parabola y = x, the limit (x, y)→(0, 0) lim f(x, y) = |. Therefore lim f(x, у) (х, у) — (0, 0) (х, у) — (0, 0)
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