Consider the function f(r.y) = %3D r+y for r +y # 0. Show that as we approach (0,0) along the x-axis the limit is 1. Show that as we approach (0,0) along the y-axis the limit is -1. Conclude that lim (r,y)→(0,0) I+y does not exist.
Consider the function f(r.y) = %3D r+y for r +y # 0. Show that as we approach (0,0) along the x-axis the limit is 1. Show that as we approach (0,0) along the y-axis the limit is -1. Conclude that lim (r,y)→(0,0) I+y does not exist.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![Consider the function
f (x, y)
= =-4
r+y
for r + y # 0.
Show that as we approach (0,0) along the r-axis the limit is 1.
Show that as we approach (0,0) along the y-axis the limit is -1.
Conclude that
lim (r.y)→(0,0) z+y
does not exist.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe1ce3ee-9943-4672-ac98-a0fbedd4e0d2%2Fe5ad0230-41e4-42c7-b896-9bd4ce84aa4c%2Fh94zo4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the function
f (x, y)
= =-4
r+y
for r + y # 0.
Show that as we approach (0,0) along the r-axis the limit is 1.
Show that as we approach (0,0) along the y-axis the limit is -1.
Conclude that
lim (r.y)→(0,0) z+y
does not exist.
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