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16y¹ fit+22 (x,y) → (0,0) (b) lim (0'0) ← (¹x)

16y¹ fit+22 (x,y) → (0,0) (b) lim (0'0) ← (¹x)

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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**Problem Statement:** Determine whether the limit exists. If so, find its value. **(a)** \[ \lim_{(x,y) \to (0,0)} \frac{x^4 - 10y^4}{x^2 + 4y^2} \] **(b)** \[ \lim_{(x,y) \to (0,0)} \frac{x^{10}y}{x^{10} + y^2} \] These problems involve evaluating the limits of multi-variable functions as the variables approach the origin (0,0). To determine whether the limit exists, approaches such as substituting specific paths (e.g., along x-axis or y-axis) or polar coordinates transformation can be used.
Transcribed Image Text:**Problem Statement:** Determine whether the limit exists. If so, find its value. **(a)** \[ \lim_{(x,y) \to (0,0)} \frac{x^4 - 10y^4}{x^2 + 4y^2} \] **(b)** \[ \lim_{(x,y) \to (0,0)} \frac{x^{10}y}{x^{10} + y^2} \] These problems involve evaluating the limits of multi-variable functions as the variables approach the origin (0,0). To determine whether the limit exists, approaches such as substituting specific paths (e.g., along x-axis or y-axis) or polar coordinates transformation can be used.
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