"Lim as x approaches 0" refers to the limit of a function as the input value, x, gets closer and closer to 0. It is used to determine the behavior of a function near a specific point.
Computing the limit as x approaches 0 allows us to understand the behavior of a function at a critical point. It can help us determine if the function is continuous, has a vertical asymptote, or has a removable discontinuity at that point.
To compute the limit as x approaches 0, you can either use algebraic manipulation or graphing to evaluate the function at values closer and closer to 0. Alternatively, you can use L'Hopital's rule, which states that the limit of the quotient of two functions is equal to the limit of their derivatives.
If the limit as x approaches 0 is undefined, it means that the function does not have a defined value at that point. This could be due to a vertical asymptote or a removable discontinuity. Further analysis is needed to determine the behavior of the function at that point.
In some cases, the limit as x approaches 0 may not exist. This could be due to the function approaching different values from the left and right sides of 0, or oscillating infinitely. In such cases, the limit is said to be undefined.