How can I calculate $\frac{\tan (\pi \cdot x)}{(x+2)}$ as $x \to -2$ without the rule of L'Hopital? When I try, I get infinity... But the correct answer is $\pi$
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I split the tan into sin/cos and multiply and divide by $2 \cos(\pi \cdot x)$, so I get $\cos (\pi \cdot x \cdot 2)$ above and $(2 \cos( \pi \cdot x)^2) \cdot (x+2)$ below. So I become 1/0 and thus infinity...