Say we have a 2-variable function f(x,y) which is not defined at (x,y)=(0,0). I wanted to make this a continuous function in (0,0) by defining it to be of a certain value at this point. If the function was a single variable, I'd set it's value at x=0 equal to the limit of the function as x approaches 0. What is the equivalent method for above when it comes to 2 variables? Is it simply the limit as x,y approach 0,0? How would one calculate this limit, and if it didn't exist, would it be impossible to make f(x,y) continuous on (0,0)? An example of f(x,y): sin(x)/x2+y2

Say we have a 2-variable function f(x,y) which is not defined at (x,y)=(0,0). I wanted to make this a continuous function in (0,0) by defining it to be of a certain value at this point. If the function was a single variable, I'd set it's value at x=0 equal to the limit of the function as x approaches 0. What is the equivalent method for above when it comes to 2 variables? Is it simply the limit as x,y approach 0,0? How would one calculate this limit, and if it didn't exist, would it be impossible to make f(x,y) continuous on (0,0)? An example of f(x,y): sin(x)/x2+y2

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

See similar textbooks