Question

${lim}_{x\to 0}\frac{tanmx}{tannx}$

Answer 1

${lim}_{x\to 0}\frac{tanmx}{tannx}$

$=\frac{{lim}_{x\to 0}tanmx}{li{m}_{x\to 0}tannx}$

$=\frac{{lim}_{mx\to 0}\frac{tanmx}{mx}\times mx}{{lim}_{nx\to 0}\frac{tannx}{nx}\times nx}$

$[\because Ifx\to 0thenmx\to alsonx\to 0]$

$=\frac{1\times m}{1\times n}[\because {lim}_{x\to 0}\frac{tanx}{x}=1]$

$=\frac{m}{n}$