9z 21. Answer the following questions given the function f below. xy if (x.y) # (0,0) f(x,y) = x+y? if (x.y) = (0,0) a. Is f continuous at (0,0)? b. Is f differentiable at (0,0)? c. If possible, evaluate f, (0,0) and f, (0,0). d. Determine whether f, and fy are continuous at (0,0). a. f(x.y) (1) - continuous at (0,0).
9z 21. Answer the following questions given the function f below. xy if (x.y) # (0,0) f(x,y) = x+y? if (x.y) = (0,0) a. Is f continuous at (0,0)? b. Is f differentiable at (0,0)? c. If possible, evaluate f, (0,0) and f, (0,0). d. Determine whether f, and fy are continuous at (0,0). a. f(x.y) (1) - 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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Transcribed Image Text:9z
21. Answer the following questions given the functionf below.
ху
if (x,y)# (0,0)
f(x,y) =
if (x.y) = (0,0)
a. Is f continuous at (0,0)?
b. Is f differentiable at (0,0)?
c. If possible, evaluate f, (0,0) and f,(0,0).
d. Determine whether f, and f, are continuous at (0,0).
a. f(x.y) (1)
continuous at (0,0).
b. f(x,y) (2).
differentiable at (0,0).
c. If possible, evaluate f, (0,0). Select the correct choice below and, if necessary, fill in the answer box to complete your
choice.
OA. f,(0,0)=
(Simplify your answer.)
O B. It is not possible to evaluate f, (0,0).
If possible, evaluate f,(0,0). Select the correct choice below and, if necessary, fill in the answer box to complete your
choice.
O A. f,(0,0)=
(Simplify your answer.)
O B. It is not possible to evaluate fy(0,0).
d. Determine whether f, and f, are continuous at (0,0). Choose the correct answer below.
O A. f, is continuous at (0,0), but fy is not continuous at (0,0).
O B. f, is continuous at (0,0), but f, is not continuous at (0,0).
O C. Both fy and fy are continuous at (0,0).
O D. Neither f, nor f, are continuous at (0,0).
(1) O is not
(2) O is not
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