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Question
Evaluate the following one sided limit:
\[\lim_{x \to - 8^+} \frac{2x}{x + 8}\]
Solution
\[\lim_{x \to - 8^+} \left( \frac{2x}{x + 8} \right)\]
\[\text{ Let }x = - 8 + h, \text{ where } h \to 0 . \]
\[ \Rightarrow \lim_{h \to 0} \left( \frac{2\left( - 8 + h \right)}{- 8 + h + 8} \right)\]
\[ = \lim_{h \to 0} \left( \frac{- 16 + 2h}{h} \right)\]
\[ = - \infty\]
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