$1)\quad\lim\limits_{x\to 0}\dfrac{\tan2x\tan4x\tan6x}{\sin x\sin3x\sin5x}$
$=\lim\limits_{x\to 0}\dfrac{\sin2x\sin4x\sin6x}{\cos2x\cos4x\cos6x\sin x\sin3x\sin5x}$
$= \lim\limits_{x\to 0}\dfrac{\dfrac{\sin2x}{2x}\cdot\dfrac{\sin4x}{4x}\cdot\dfrac{\sin6x}{6x}\cdot 48x^3}{\cos2x.\cos4x.\cos6x.\dfrac{\sin x}{x}\cdot\dfrac{\sin3x}{3x}\cdot\dfrac{\sin5x}{5x}\cdot 15x^3}$
$= \lim\limits_{x\to 0}\dfrac{1.1.1.48}{\cos2x.\cos4x.\cos6x.1.1.1.15}$
$=\lim\limits_{x\to 0}\dfrac{16}{\cos0.\cos0.\cos0.5}$
$=\dfrac{16}{5}$
$2)\quad \lim\limits_{x\to \infty}\dfrac{n^2 + 2\ln n + 6.2^n}{-5n^2 + \ln n+ 3.2^n}$
$= \lim\limits_{x\to \infty}\dfrac{\dfrac{n^2}{2^n} + 2\cdot\dfrac{\ln n}{2^n} + 6}{-5\cdot\dfrac{n^2}{2^n} +\dfrac{\ln n}{2^n} + 3}$
$= \dfrac{0 + 2.0 + 6}{-5.0 + 0 + 3}$
$= 2$
