In calculus, we often encounter limits that approach a specific value from either the left (negative side) or the right (positive side) of that value. These limits are known as one-sided limits. Unlike two-sided limits, one-sided limits only consider the behavior of a function as it approaches the given value from a particular direction.

Continuity, on the other hand, refers to the smoothness and connectedness of a function's graph. A function is said to be continuous at a point if its value at that point is equal to the limit of the function as it approaches that point from both sides.

For example, let's consider the function f(x) = |x|. As x approaches 0 from the left (x < 0), the limit of f(x) is -x. However, as x approaches 0 from the right (x > 0), the limit of f(x) is x. Since these one-sided limits are not equal, the function f(x) = |x| is not continuous at x = 0.

Understanding one-sided limits and continuity is essential in analyzing the behavior of functions and solving calculus problems.