Question

lim as x->0 2t/tan(t). Is it 0?

Answer 1

\[\lim_{x \rightarrow 0} 2x \div \tan(x)=\lim_{x \rightarrow 0}2x \div \frac{\sin(x)}{\cos(x)}\]
\[=\lim_{x \rightarrow 0}2x \cdot \frac{\cos(x)}{\sin(x)}=\lim_{x \rightarrow 0}2 \cdot \frac{x}{\sin(x)} \cdot \cos(x)\]
\[=2(1)(\cos(0))=2(1)(1)=2\]