Question

limit of cot2x/cotx as X approaches 0?

Answer 1

Use the l'Hopital's rule, two times.

$\lim_{x\rightarrow0} \frac{\cot(2x)}{\cot(x)}=\lim_{x\rightarrow0} \frac{2\sin^2(x)}{\sin(x)}=\lim_{x\rightarrow0} \frac{4(\cos^2(x)-\sin^2(x))}{8(\cos^2(2x)-sin^2(2x))} = \frac{1}{2}$

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