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
t10
![**Problem Statement:**
Evaluate the limit, or type "DNE" if the limit Does Not Exist:
\[
\lim_{(x,y) \to (1,1)} \frac{9x^{12} - 9y^{12}}{3x^6 + 3y^6} = \boxed{}
\]
**Explanation:**
This problem asks you to evaluate the limit of a function as the point \((x, y)\) approaches \((1, 1)\). The expression contains a fraction with a polynomial in the numerator and denominator. You must simplify or apply limit theorems to determine if the limit exists or if it does not. If the limit does not exist, indicate this with "DNE."](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4e39a1d0-143c-41f0-ae59-e967e0535bad%2F6e8d852c-be46-4f1a-a54c-ba3f24e59ef7%2Fvuu5319_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Evaluate the limit, or type "DNE" if the limit Does Not Exist:
\[
\lim_{(x,y) \to (1,1)} \frac{9x^{12} - 9y^{12}}{3x^6 + 3y^6} = \boxed{}
\]
**Explanation:**
This problem asks you to evaluate the limit of a function as the point \((x, y)\) approaches \((1, 1)\). The expression contains a fraction with a polynomial in the numerator and denominator. You must simplify or apply limit theorems to determine if the limit exists or if it does not. If the limit does not exist, indicate this with "DNE."
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