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3x2 + 1?y? + 3y? + 3z2 3 Show that lim (1,y,2)+(0,0,0) 1² + y? + z²

3x2 + 1?y? + 3y? + 3z2 3 Show that lim (1,y,2)+(0,0,0) 1² + y? + z²

Calculus: Early Transcendentals
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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Question
Show that \[ \lim_{(x, y, z) \to (0, 0, 0)} \frac{3x^2 + x^2y^2 + 3y^2 + 3z^2}{x^2 + y^2 + z^2} = 3 \] This expression asks us to find the limit of a multivariable function as the point \((x, y, z)\) approaches \((0, 0, 0)\). The function involves a rational expression that contains quadratic terms in the numerator and denominator. The goal is to show that this limit evaluates to \(3\).
Transcribed Image Text:Show that \[ \lim_{(x, y, z) \to (0, 0, 0)} \frac{3x^2 + x^2y^2 + 3y^2 + 3z^2}{x^2 + y^2 + z^2} = 3 \] This expression asks us to find the limit of a multivariable function as the point \((x, y, z)\) approaches \((0, 0, 0)\). The function involves a rational expression that contains quadratic terms in the numerator and denominator. The goal is to show that this limit evaluates to \(3\).
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