144k views
7 votes
Answer the following True or False:

If lim f(x) = – 3 then f(x) is continuous at x = – 2.
2 - 2

User Joostblack
by
8.6k points

1 Answer

0 votes

False; consider as a counterexample the function f : ℝ→ℝ defined by


f(x)=\begin{cases}-3&\text{for }x\\eq2\\0&\text{for }x=2\end{cases}

Clearly f approaches -3 as x gets closer to -2, but neither limit from either side is equal to the function's value at x = 2 (that is, -3 ≠ 0), so f is not continuous.

User Afroz Alam
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories