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\lim_{t o -1} E(t) = \lim_{t o -1} (t + 3) = -1 + 3 = 2
Although $ E(t) $ is undefined at $ t = -1 $, the limit exists.
Question: An astronomer models the orbital period $ T $ of a planet around a star as $ T = k \cdot r^{3/2} $, where $ r $ is the semi-major axis and $ k $ is a constant. If $ T = 8 $ when $ r = 4 $, find $ T $ when $ r = 9 $.

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📰 x = \frac{6 \pm \sqrt{(-6)^2 - 4 \cdot 3 \cdot 2}}{2 \cdot 3} = \frac{6 \pm \sqrt{36 - 24}}{6} = \frac{6 \pm \sqrt{12}}{6} = \frac{6 \pm 2\sqrt{3}}{6} = 1 \pm \frac{\sqrt{3}}{3} 📰 The sum of the roots is: 📰 \left(1 + \frac{\sqrt{3}}{3}\right) + \left(1 - \frac{\sqrt{3}}{3}\right) = 2