Final answer:
To find the limit of a function, we evaluate the function at values that approach the given value. If the function approaches a specific value, that value is the limit. If not, the limit does not exist.
Step-by-step explanation:
The limit of a function represents the value that the function approaches as the input approaches a certain value. To find the limit, we can evaluate the function at different values that are closer and closer to the given value. If the function approaches a specific value as the input approaches the given value, then that specific value is the limit.
For example, let's say we have the function f(x) = x^2. If we want to find the limit as x approaches 3, we can evaluate the function for different values of x that are closer and closer to 3, such as 2.9, 2.99, and so on. As we plug in these values, we can observe that f(x) approaches 9 as x approaches 3. Therefore, the limit of f(x) as x approaches 3 is 9.
If the function does not approach a specific value as the input approaches the given value, then the limit does not exist (denoted as 'dne').