tiny-tim said:hi mathe! welcome to pf!
show us what you've tried, and where you're stuck, and then we'll know how to help!
)mathe said:
The limit of a function of more than one variable is the value that a function approaches as its input variables approach a certain point. It is a fundamental concept in calculus and is used to determine the behavior of a function near a certain point.
The limit of a function of more than one variable can be calculated by taking the limit of the function along different paths approaching the point of interest. If the limit is the same regardless of the path, then it can be said that the function has a limit at that point.
The limit of a function is the value that the function approaches as its input variables approach a certain point, while the value of a function is the actual output of the function at a given point. The limit may or may not be equal to the value of the function at that point.
Yes, the limit of a function of more than one variable can exist at a point where the function is not defined. This is because the limit is determined by the behavior of the function near the point of interest, not necessarily at the point itself.
The limit of a function of more than one variable is used in many real-world applications, such as in engineering, physics, and economics. It is used to model and predict the behavior of complex systems and to optimize functions with multiple variables.