Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Please give correct answer. Only one part left for the problem, everything else is correct.

7x y
Examine the behavior of f(x, y)
as (æ, y) approaches (0,0).
6x4 + y?
Use "infinity" for "o" and "-infinity" for "-o". Use "DNE" for "Does not exist".
(a) Taking a linear approach to the origin along the y-axis, we find
lim
(x,y)→(0,0), x=0
7x?y
6x4 + y?
(b) Taking a linear approach to the origin along the x-axis, we find
lim
(x,y)→(0,0), y=0
6x4 + y2
(c) Taking a linear approach to the origin along a line y = mx with m + 0 we find
7x?y
6x4 + y2
lim
lim
(x,y)→(0,0), y=mx
m
Thought question: Do your answers to parts (a)-(c) allow you to conclude that the limit exists?
(d) Taking an approach to the origin along the parabola y = x²
find
we
Tæ?y
6x4 + y?
7
lim
(x,y)→(0,0), y=x²
= lim
x→0
7
(e) Find the value of the limit. Be sure you can explain your answer.
7x?y
lim
(x,y)→(0,0)
DNE
6x4 + y?
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Transcribed Image Text:7x y Examine the behavior of f(x, y) as (æ, y) approaches (0,0). 6x4 + y? Use "infinity" for "o" and "-infinity" for "-o". Use "DNE" for "Does not exist". (a) Taking a linear approach to the origin along the y-axis, we find lim (x,y)→(0,0), x=0 7x?y 6x4 + y? (b) Taking a linear approach to the origin along the x-axis, we find lim (x,y)→(0,0), y=0 6x4 + y2 (c) Taking a linear approach to the origin along a line y = mx with m + 0 we find 7x?y 6x4 + y2 lim lim (x,y)→(0,0), y=mx m Thought question: Do your answers to parts (a)-(c) allow you to conclude that the limit exists? (d) Taking an approach to the origin along the parabola y = x² find we Tæ?y 6x4 + y? 7 lim (x,y)→(0,0), y=x² = lim x→0 7 (e) Find the value of the limit. Be sure you can explain your answer. 7x?y lim (x,y)→(0,0) DNE 6x4 + y?
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