- #1
lukasz08
- 10
- 0
find the points of discontinuouty
limit as x,y ---> (0,0) of function f(x,y) = 1-((cos(x^2+y^2)/(x^2+y^2))
limit as x,y ---> (0,0) of function f(x,y) = 1-((cos(x^2+y^2)/(x^2+y^2))
A limit of a function of two variables is a value that a function approaches as the two variables approach a specific point on the function's domain. It represents the behavior of the function near that point and can be used to determine continuity, differentiability, and other properties of the function.
To evaluate a limit of a function of two variables, you can use the same techniques as for a function of one variable. You can substitute values for the two variables and observe the resulting output values, or you can use algebraic techniques such as factoring, rationalizing, and simplifying to find the limit.
The main difference between a limit of a function of two variables and a limit of a function of one variable is that the former involves two independent variables, while the latter only has one. This means that the behavior of the function near a specific point depends on the values of both variables, rather than just one.
Yes, a limit of a function of two variables can exist even if the function is not defined at that point. This is because the limit only considers the behavior of the function near the point, not the actual value at the point itself. However, if the limit does not exist, it also means that the function is not defined at that point.
The concept of a limit of a function of two variables is used in many real-life applications, particularly in fields such as physics, engineering, and economics. It can be used to model and predict the behavior of complex systems with multiple variables, such as fluid flow, heat transfer, and optimization problems.