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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F304238c1-892d-4f66-90f4-8d5405bfbe58%2F3aa6c79a-0a29-4337-8bea-5339196f423a%2F1cs3e1n_processed.jpeg&w=3840&q=75)
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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