Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Answer the following True or False:
If lim f(x) = – 3 then f(x) is continuous at x = – 2.
2 - 2


Sagot :

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

[tex]f(x)=\begin{cases}-3&\text{for }x\neq2\\0&\text{for }x=2\end{cases}[/tex]

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.