Complete the following sentences in terms of a limit.


b. A function is continuous from the right at a if _____ .

Verified step by step guidance

1. To understand continuity from the right at a point 'a', we need to consider the behavior of the function as it approaches 'a' from the right side.
2. The formal definition of right-hand continuity at a point 'a' involves the concept of limits. Specifically, we need to evaluate the limit of the function as the input approaches 'a' from values greater than 'a'.
3. Mathematically, this is expressed as \( \lim_{{x \to a^+}} f(x) \), where \( x \to a^+ \) indicates that 'x' is approaching 'a' from the right.
4. For the function to be continuous from the right at 'a', the limit \( \lim_{{x \to a^+}} f(x) \) must equal the function value at 'a', which is \( f(a) \).
5. Thus, the sentence can be completed as: A function is continuous from the right at 'a' if \( \lim_{{x \to a^+}} f(x) = f(a) \).