Which of the following expressions represents the concept of continuity in calculus?

The expression that represents the concept of continuity in calculus is centered around the idea that a function behaves predictably at a certain point. Specifically, for a function ( f(x) ) to be continuous at a point ( a ), three criteria must be satisfied. First, the function must be defined at that point, meaning ( f(a) ) must exist. Second, the limit of the function as ( x ) approaches ( a ) must exist, which leads to the third requirement: the value of that limit must equal the value of the function at that point. Thus, the expression ( \lim_{x \to a} f(x) = f(a) ) captures these criteria succinctly. It establishes that the limit of the function as it approaches ( a ) equals the actual function value at ( a ), confirming that there are no jumps, breaks, or holes in the function at that point, which is the essence of continuity.