Extension: One-Sided Continuities
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Problems 4
- Does {1−x3x<2(x−3)2−8x≥2\begin{cases}1-x^3&x<2\\(x-3)^2-8&x\geq2\end{cases}{1−x3(x−3)2−8x<2x≥2 have a one sided continuity?
- Does {3x2−6x<02−(x−2)3x≥0\begin{cases}3x^2-6&x<0\\2-(x-2)^3&x\geq0\end{cases}{3x2−62−(x−2)3x<0x≥0 have a one sided continuity?
- Does x\sqrt{x}x have a one sided continuity?
- Which side does {−2x+4x≤23x−8x>2\begin{cases}-2x+4&x\leq2\\3x-8&x>2\end{cases}{−2x+43x−8x≤2x>2 have a discontinuity?