Science:Math Exam Resources/Courses/MATH110/December 2014/Question 03 (c)/Statement

Which one of the following statements is the best reason why ${\textstyle f(x)}$ is continuous at ${\textstyle x=4}$?

(i) ${\textstyle f(4)}$ exists.

(ii) ${\textstyle \displaystyle \lim _{x\to 4}f(x)}$ exists.

(iii) Both (i) and (ii).

(iv) ${\textstyle f(4)}$ and ${\textstyle \displaystyle \lim _{x\to 4}f(x)}$ exist, and they are equal.