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

Sagot :

LammettHashidn

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.

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