text: Your question is a bit vague. The study of limits is formalized by the epsilon-delta definition that one learns in introductory calculus, but limits aren't really found that way. Instead, one presupposes a limit using other methods and then proves that limit (or disproves it as may be the case) using the definition. Thus, a possible problem in learning limits may be inexperience with the behavior of functions and series/sequences, but that is easily overcome.\nIf, on the other hand, you're referring to problems that may occur when studying the limit of a function at a point, the largest problem is that limits at the point taken along different directions are not the same, and thus we say the limit of the function at that point does not exist. \nAnother problem is that the limit may exist at the point, but the value of the function at that point is not the same as the limit of the function at that point. When this occurs, we say that the function is not continuous at the point in question.\nThe only other problem is that the limit of the function may not exist due to the function diverging at that point (as one approaches the point from each direction, the value of the function increases or decreases without bound).