so... using L'Hopital rule, LH, since this one is a indeterminate type
[tex]\bf \lim\limits_{x\to 0}~\cfrac{tan(7x)}{sin(3x)}\implies \underline{LH}\quad \lim\limits_{x\to 0}~\cfrac{7sec^2(7x)}{cos(3x)}\implies \cfrac{7\cdot \frac{1}{cos^2(7x)}}{cos(3x)}
\\\\\\
\lim\limits_{x\to 0}~\cfrac{7\cdot \frac{1}{cos^2(0)}}{cos(0)}\implies \cfrac{7\cdot \frac{1}{1}}{1}\implies 7[/tex]
