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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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.
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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