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ped 9) Given f(x,y)=x² + y² use Algebra to find a) lim f(x+Ax,y)-f(x,y) Ar-0 Ar b) lim Ay0 f(x,y+Ay)-f(x,y) Ay

ped 9) Given f(x,y)=x² + y² use Algebra to find a) lim f(x+Ax,y)-f(x,y) Ar-0 Ar b) lim Ay0 f(x,y+Ay)-f(x,y) Ay

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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I need help with this calc question
**Problem 8** is an algebra/limit problem which illustrates the power rule of derivatives being "derived" from the limit process. Most of you can see the answers without doing the algebra/limit process. I would like you to show the work that gives the answers without using the power rule. It is nice to give credit to those brilliant mathematicians (Newton and Leibniz) who developed calculus. The concept of limits has been around for over 2000 years but derivatives were developed in 1700. 9) Given \( f(x, y) = x^2 + y^2 \) use Algebra to find a) \(\lim_{\Delta x \to 0} \frac{f(x + \Delta x, y) - f(x, y)}{\Delta x} \) b) \(\lim_{\Delta y \to 0} \frac{f(x, y + \Delta y) - f(x, y)}{\Delta y} \)
Transcribed Image Text:**Problem 8** is an algebra/limit problem which illustrates the power rule of derivatives being "derived" from the limit process. Most of you can see the answers without doing the algebra/limit process. I would like you to show the work that gives the answers without using the power rule. It is nice to give credit to those brilliant mathematicians (Newton and Leibniz) who developed calculus. The concept of limits has been around for over 2000 years but derivatives were developed in 1700. 9) Given \( f(x, y) = x^2 + y^2 \) use Algebra to find a) \(\lim_{\Delta x \to 0} \frac{f(x + \Delta x, y) - f(x, y)}{\Delta x} \) b) \(\lim_{\Delta y \to 0} \frac{f(x, y + \Delta y) - f(x, y)}{\Delta y} \)
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