munkhuu1 said:
tiny-tim said:hi munkhuu1!
almost
the limit of a product (or quotient) is the product (or quotient) of the limits if they exist,
so you also need to point out that the two limits exist
The limit of multi variable refers to the value that a function approaches as the input variables approach a specific point or value. It is a fundamental concept in calculus and is used to describe the behavior of a function near a given point.
The limit of a single variable only considers the behavior of a function along a single axis, while the limit of multi variable takes into account the behavior of a function along multiple axes. This allows for a more comprehensive understanding of a function's behavior near a given point.
Yes, it is possible for the limit of multi variable to exist even if the limit of each individual variable does not. This is because the behavior of a function can be affected by the interaction of multiple variables, even if each individual variable does not have a well-defined limit.
The limit of multi variable is typically calculated by evaluating the function at different points near the given point and observing the trend of the function's values as the input variables get closer to the given point. This can be done numerically or graphically.
The limit of multi variable has many applications in science, particularly in physics and engineering, where it is used to analyze the behavior of systems with multiple variables. It is also used in optimization problems and in the study of complex systems such as weather patterns and population dynamics.