se the function to show that fx(0, 0) and fy(0, 0) both exist, but that f is not differentiable at ( 7x²y x4 + y2 0, (x, y) # (0, 0) f(x, y) = (x, y) = (0, 0) %3D fx(0, 0) = fy(0, 0) = lim along the line y = x (x, y) (0, 0) long the curve y = x2 lim (x, y) - (0, 0) O fis continuous at (0, 0) O fis not continuous at (0, 0)

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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Use the function to show that f,(0, 0) and fy(0, 0) both exist, but that f is not differentiable at (0, 0).
7x3y
x4 + y2
0,
f(x, y) =
(x, y) # (0, 0)
(х, у) %3D (0, 0)
=
fx(0, 0) =
fy(0, 0) =
Along the line
lim
(x, y) → (0, 0)
y = x
Along the curve
y = x2
lim
(x, y) → (0, 0)
O f is continuous at (0, 0)
O f is not continuous at (0, 0)
Transcribed Image Text:Use the function to show that f,(0, 0) and fy(0, 0) both exist, but that f is not differentiable at (0, 0). 7x3y x4 + y2 0, f(x, y) = (x, y) # (0, 0) (х, у) %3D (0, 0) = fx(0, 0) = fy(0, 0) = Along the line lim (x, y) → (0, 0) y = x Along the curve y = x2 lim (x, y) → (0, 0) O f is continuous at (0, 0) O f is not continuous at (0, 0)
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