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In this problem we show that the function lim (1,42)→(0,0) does not have a limit as (x, y) → (0,0). (a) Suppose that we consider (x,y) → (0,0) along the curve y = 4x. Find the limit in this case: 4x-y x+y lim (2,52)→(0,0) = (b) Now consider (x,y) → (0,0) along the curve y = 5x. Find the limit in this case: 42-y x+y f(x, y) 4x-y z+y lim (x,ma)→(0,0) (Be sure that (c) Note that the results from (a) and (b) indicate that f has no limit as (x,y) → (0, 0) (be sure you can explain why!). To show this more generally, consider (x, y) → (0,0) along the curve y = mx, for arbitrary m. Find the limit in this case: 9. 4x - y x+y you can explain how this result also indicates that f has no limit as (x,y) → (0,0).

In this problem we show that the function lim (1,42)→(0,0) does not have a limit as (x, y) → (0,0). (a) Suppose that we consider (x,y) → (0,0) along the curve y = 4x. Find the limit in this case: 4x-y x+y lim (2,52)→(0,0) = (b) Now consider (x,y) → (0,0) along the curve y = 5x. Find the limit in this case: 42-y x+y f(x, y) 4x-y z+y lim (x,ma)→(0,0) (Be sure that (c) Note that the results from (a) and (b) indicate that f has no limit as (x,y) → (0, 0) (be sure you can explain why!). To show this more generally, consider (x, y) → (0,0) along the curve y = mx, for arbitrary m. Find the limit in this case: 9. 4x - y x+y you can explain how this result also indicates that f has no limit as (x,y) → (0,0).

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 91E
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In this problem we show that the function lim (x,4x)→(0,0) does not have a limit as (x,y) → (0,0). (a) Suppose that we consider (x, y) -> (0, 0) along the curve y = 4x. Find the limit in this case: f(x, y) = 4x-y x+y lim (2,5z)—(0,0) (b) Now consider (x, y) (0,0) along the curve y = 5x. Find the limit in this case: 4x-y x+y 4x - Y x + y (c) Note that the results from (a) and (b) indicate that f has no limit as (x, y) → (0,0) (be sure you can explain why!). To show this more generally, consider (x, y) →> (0,0) along the curve y = mx, for arbitrary m. Find the limit in this case: 9. 4r-y lim (x,mx)→(0,0) +y (Be sure that you can explain how this result also indicates that f has no limit as (x,y) → (0,0).
Transcribed Image Text:In this problem we show that the function lim (x,4x)→(0,0) does not have a limit as (x,y) → (0,0). (a) Suppose that we consider (x, y) -> (0, 0) along the curve y = 4x. Find the limit in this case: f(x, y) = 4x-y x+y lim (2,5z)—(0,0) (b) Now consider (x, y) (0,0) along the curve y = 5x. Find the limit in this case: 4x-y x+y 4x - Y x + y (c) Note that the results from (a) and (b) indicate that f has no limit as (x, y) → (0,0) (be sure you can explain why!). To show this more generally, consider (x, y) →> (0,0) along the curve y = mx, for arbitrary m. Find the limit in this case: 9. 4r-y lim (x,mx)→(0,0) +y (Be sure that you can explain how this result also indicates that f has no limit as (x,y) → (0,0).
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