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yA - 2x? lim 4 - 2х 2 (х., у)- (0,0) у +х 4

yA - 2x? lim 4 - 2х 2 (х., у)- (0,0) у +х 4

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Use the​ two-path test to prove that the following limit does not exist.

Use the two-path test to prove that the following limit does not exist. 4 2 y" - 2x lim 4 (х,у) —> (0,0) у" +x* y - 2x2 What value does f(x,y) = approach as (x,y) approaches (0,0) along the x-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. +x A. f(x,y) approaches (Simplify your answer.) B. f(x,y) approaches co. С. f{x,у) аpprоaches - со. D. f(x,y) has no limit as (x,y) approaches (0,0) along the x-axis. y - 2x2 What value does f(x,y) = 4 y* +x approach as (x,y) approaches (0,0) along the y-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. f(x,y) approaches |. (Simplify your answer.) В. f(х,у) аpproaches oo. С. f{\x,у) аpproaches - 00. D. f(x,y) has no limit as (x,y) approaches (0,0) along the y-axis. Why does the given limit not exist? A. As (x,y) approaches (0,0) along different paths, f(x,y) does not always approach a finite value. B. As (x,y) approaches (0,0) along different paths, f(x,y) approaches two different values. C. As (x,y) approaches (0,0) along different paths, f(x,y) always approaches the same value.
Transcribed Image Text:Use the two-path test to prove that the following limit does not exist. 4 2 y" - 2x lim 4 (х,у) —> (0,0) у" +x* y - 2x2 What value does f(x,y) = approach as (x,y) approaches (0,0) along the x-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. +x A. f(x,y) approaches (Simplify your answer.) B. f(x,y) approaches co. С. f{x,у) аpprоaches - со. D. f(x,y) has no limit as (x,y) approaches (0,0) along the x-axis. y - 2x2 What value does f(x,y) = 4 y* +x approach as (x,y) approaches (0,0) along the y-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. f(x,y) approaches |. (Simplify your answer.) В. f(х,у) аpproaches oo. С. f{\x,у) аpproaches - 00. D. f(x,y) has no limit as (x,y) approaches (0,0) along the y-axis. Why does the given limit not exist? A. As (x,y) approaches (0,0) along different paths, f(x,y) does not always approach a finite value. B. As (x,y) approaches (0,0) along different paths, f(x,y) approaches two different values. C. As (x,y) approaches (0,0) along different paths, f(x,y) always approaches the same value.
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