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

Which one of the following statements is the best reason why ${\textstyle f(x)}$ is not continuous at ${\textstyle x=0}$?

(i) ${\textstyle f(0)}$ does not exist.

(ii) ${\textstyle \displaystyle \lim _{x\to 0}f(x)}$ does not exist.

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

(iv) ${\textstyle f(0)}$ and ${\textstyle \displaystyle \lim _{x\to 0}f(x)}$ exist, but they are not equal.