Solution Found!
Filling in a function value The domain of f(x,y) =
Chapter 9, Problem 67AE(choose chapter or problem)
Filling in a function value The domain of \(f(x, y)=e^{-1 /\left(x^{2}+y^{2}\right)}\) excludes (0,0). How should f be defined at (0,0) to make it continuous there?
Questions & Answers
QUESTION:
Filling in a function value The domain of \(f(x, y)=e^{-1 /\left(x^{2}+y^{2}\right)}\) excludes (0,0). How should f be defined at (0,0) to make it continuous there?
ANSWER:Solution 67AE
Step 1 of 2:
Given function is f(x,y) =
Continuous definition:
A function f is said to be continuous at (a,b) means f is defined at (a , b) and f(x,y) = f(a,b).
That is , the given function f is continuous .
So , f(x,y) = f(0,0)
f(x,y) =
Path x= 0 , then f(x,y) =
=
=
=
= =
=
= 0
Therefore , f(x,y) =
= 0