Yes, there are several ways to understand the concept of a limit in calculus without going into the details of a formal proof. One way to understand the concept of a limit is to think of it as a way to measure how close a function gets to a particular value as the input to the function gets closer and closer to a certain number. For example, if we have a function f(x) and we want to find the limit of the function as x approaches 2, we can think of this as asking "how close does f(x) get to a certain number as x gets closer and closer to 2?"
Another way to understand the concept of a limit is to think of it as a way to describe the behavior of a function as the input gets very large or very small. For example, if we have a function f(x) and we want to find the limit of the function as x approaches infinity, we can think of this as asking "how does f(x) behave as x gets very large?"
Overall, the concept of a limit is a fundamental concept in calculus that allows us to describe and analyze the behavior of functions as the input to the function changes. While a formal proof of the limit can be quite complex, there are several intuitive ways to understand the concept without going into the details of the proof.