I was actually more prepared for the Hubbard Hamiltonian than for regular calculusPeroK said:
For one thing, you can't just substitute ##\infty## into the expression. For another thing, the expression above has the form ##[\infty - \infty]##, which is one of several indeterminate forms, along with ##[\frac0 0]##, ##[\frac{\infty}{\infty}]## and a few others.supernano said:
supernano said:
The limit of large but finite refers to the value that a function approaches as the input approaches a very large number, but remains finite. It is a way to describe the behavior of a function as the input gets closer and closer to infinity.
The limit of large but finite is a specific type of limit where the input approaches infinity but remains finite. The limit at infinity, on the other hand, refers to the behavior of a function as the input reaches infinity without any restrictions on its finiteness.
No, the limit of large but finite cannot be infinite. As the input approaches infinity, the value of the function may become very large, but it will still be a finite value. The limit at infinity, however, can be infinite if the function grows without bound as the input approaches infinity.
The limit of large but finite can be calculated using the same methods as any other limit. This includes substitution, factoring, and using algebraic manipulations. However, it is important to consider the behavior of the function as the input approaches infinity, and whether it remains finite or approaches infinity itself.
The limit of large but finite is important because it helps us understand the behavior of functions as they approach very large numbers. This can be useful in modeling real-world phenomena, such as population growth, where the input (time) can become very large, but the population size remains finite. It also has applications in calculus, where it is used to find the area under curves and calculate rates of change.