A limit can be defined as the value that a function or sequence approaches as the input or index approaches a certain point. It represents the behavior or trend of the function or sequence near that particular point.

Explanation: Here, the given image shows the limit of a function of x equals A as and when x approaches a.

Continuity, in the context of mathematics and functions, refers to the smooth and unbroken nature of a function’s graph or behavior. It implies that there are no abrupt jumps, breaks, or holes in the graph of the function within a certain interval or over its entire domain.

More formally, a function f(x) is considered continuous at a point x = a if three conditions are satisfied.

Explanation: Here, the given image shows the three conditions that are

If these conditions hold for every point in the domain of the function, then the function is said to be continuous over its entire domain.