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Alenkinab [10]
2 years ago
15

Answer the following True or False:

Mathematics
1 answer:
Ilia_Sergeevich [38]2 years ago
4 0

False; consider as a counterexample the function <em>f</em> : ℝ→ℝ defined by

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

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

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