Use the two-path test to prove that the following limit does not exist. 2x lim 4 2 (x,y)→(0,0) y +x .--.. 2 4 y - 2x 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, 4 y +x the answer box to complete your choice. O A. f(x,y) approaches (Simplify your answer.) O B. f(x,y) approaches - o. OC. f(x,y) approaches co. O D. f(x,y) has no limit as (x,y) approaches (0,0) along the x-axis. 2 y - 2x What value does f(x,y) = approach as (x,y) approaches (0,0) along the y-axis? Select the correct choice below and, if necessary, 4 2 у +х the answer box to complete your choice. O A. f(x,y) approaches . (Simplify your answer.) O B. f(x,y) approaches co. O C. f(x,y) approaches - o. O D. f(x,y) has no limit as (x,y) approaches (0,0) along the y-axis. Why does the given limit not exist? O A. As (x,y) approaches (0,0) along different paths, f(x,y) always approaches the same value. O B. As (x,y) approaches (0,0) along different paths, f(x,y) does not always approach a finite value. OC. As (x,y) approaches (0,0) along different paths, f(x,y) approaches two different values.

Use the two-path test to prove that the following limit does not exist. 2x lim 4 2 (x,y)→(0,0) y +x .--.. 2 4 y - 2x 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, 4 y +x the answer box to complete your choice. O A. f(x,y) approaches (Simplify your answer.) O B. f(x,y) approaches - o. OC. f(x,y) approaches co. O D. f(x,y) has no limit as (x,y) approaches (0,0) along the x-axis. 2 y - 2x What value does f(x,y) = approach as (x,y) approaches (0,0) along the y-axis? Select the correct choice below and, if necessary, 4 2 у +х the answer box to complete your choice. O A. f(x,y) approaches . (Simplify your answer.) O B. f(x,y) approaches co. O C. f(x,y) approaches - o. O D. f(x,y) has no limit as (x,y) approaches (0,0) along the y-axis. Why does the given limit not exist? O A. As (x,y) approaches (0,0) along different paths, f(x,y) always approaches the same value. O B. As (x,y) approaches (0,0) along different paths, f(x,y) does not always approach a finite value. OC. As (x,y) approaches (0,0) along different paths, f(x,y) approaches two different values.

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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