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