7x2 – 2y2 EXAMPLE 1 Show that lim does not exist. (x, y)-(0, 0) x² + y2 SOLUTION Let f(x, y) = (7x² – 2y²)/(x² + y²). First, let's approach (0, 0) along the x-axis. Then y = gives f(x, 0) = 7x2/x² = for all x + 0, so f(x, у) > as (x, y) → (0, 0) along the x-axis. We now approach along the y-axis by putting x = . Then f(0, y) = -2y2/y2 = for all y + 0, so f(x, у) > as (x, y) → (0, 0) along the y-axis. Since f has two different limits along two different lines, the given limit does not exist.

7x2 – 2y2 EXAMPLE 1 Show that lim does not exist. (x, y)-(0, 0) x² + y2 SOLUTION Let f(x, y) = (7x² – 2y²)/(x² + y²). First, let's approach (0, 0) along the x-axis. Then y = gives f(x, 0) = 7x2/x² = for all x + 0, so f(x, у) > as (x, y) → (0, 0) along the x-axis. We now approach along the y-axis by putting x = . Then f(0, y) = -2y2/y2 = for all y + 0, so f(x, у) > as (x, y) → (0, 0) along the y-axis. Since f has two different limits along two different lines, the given limit does not exist.

Name: 7x2 – 2y2ΕΧΑMPLE 1Show thatlimdoes not exist.(х, у) — (0, 0) х2 + у2S
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Description: 7x2 – 2y2ΕΧΑMPLE 1Show thatlimdoes not exist.(х, у) — (0, 0) х2 + у2SOLUTIONLet f(x, y) = (7x² – 2y2)/(x2 + y2). First, let's approach (0, 0) along the x-axis. Then y =givesf(x, 0) = 7x²/x² =for all x + 0, sof(x, у) —as (x, y) → (0, 0) along the x-a

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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