Limits are a fundamental concept in calculus that allow us to examine the behavior of functions as they approach a certain value. They play a crucial role in understanding the rate of change, continuity, and the concept of infinity in mathematics. We use limits to determine what happens to a function as its input approaches a particular value or as it tends towards positive or negative infinity.

To denote limits, we use a notation known as the limit notation. For example, if we want to find the limit of a function f(x) as x approaches a particular value, say c, we write it as:

Let's consider an example to understand this concept better. Suppose we have the function f(x) = x^2. We want to find the limit of f(x) as x approaches 2. By substituting values closer and closer to 2 into the function, we observe that f(x) gets arbitrarily close to 4. Therefore, we can conclude that:

Limits can also be determined graphically by analyzing the behavior of the function's graph as it approaches a specific value.

Remember, understanding limits is crucial for tackling more complex calculus concepts. Keep practicing and you'll master this topic in no time!