In this problem we show that the function f(x, y) 7x²-y² lim (2,2x)+(0,0) z²+y² 7x² - y² x² + y² does not have a limit as (x, y) → (0,0). (a) Suppose that we consider (x, y) → (0,0) along the curve y = 2x. Find the limit in this case: (b) Now consider (x, y) → (0,0) along the curve y = 3x. Find the limit in this case: 7x²-y² lim (2,3x)+(0,0) z²+y² (c) Note that the results from (a) and (b) indicate that ƒ 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: lim (z,mx)+(0,0) z²+y² 72²-y² = (Be sure that you can explain how this result also indicates that ƒ has no limit as (x, y) → (0,0).
In this problem we show that the function f(x, y) 7x²-y² lim (2,2x)+(0,0) z²+y² 7x² - y² x² + y² does not have a limit as (x, y) → (0,0). (a) Suppose that we consider (x, y) → (0,0) along the curve y = 2x. Find the limit in this case: (b) Now consider (x, y) → (0,0) along the curve y = 3x. Find the limit in this case: 7x²-y² lim (2,3x)+(0,0) z²+y² (c) Note that the results from (a) and (b) indicate that ƒ 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: lim (z,mx)+(0,0) z²+y² 72²-y² = (Be sure that you can explain how this result also indicates that ƒ has no limit as (x, y) → (0,0).
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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