3.28 関数の極限の計算

問 3.106 (関数の極限の計算)

$\displaystyle (1)\quad \lim_{x\to a} \left(c_{N}\,x^{N}+c_{N-1}\,x^{N-1}+\cdots+ c_{2}\,x^2+c_{1}\,x+c_{0}\right)$

$\displaystyle (2)\quad \lim_{x\to\infty} \frac{x^2+3x+1}{x-5}$	$\displaystyle (3)\quad \lim_{x\to-\infty} \frac{x^2-x}{2x^2+3}$	$\displaystyle (4)\quad \lim_{x\to-\infty} \frac{x^2+2}{x^5-4x^2+1}$
$\displaystyle (5)\quad \lim_{x\to+0} \frac{x+3}{x^2-1}$	$\displaystyle (6)\quad \lim_{x\to-0} \frac{x^3+2x}{x^5-3x^2}$	$\displaystyle (7)\quad \lim_{x\to-0} \frac{5x^4-x^3}{2x^3-x^2}$
$\displaystyle (8)\quad \lim_{x\to1+0} \frac{x^2-1}{x^2+x-2}$	$\displaystyle (9)\quad \lim_{x\to1+0} \frac{x^3-x^2-x+1}{x^2+x-2}$	$\displaystyle (10)\quad \lim_{x\to1+0} \frac{x^2-1}{x^3-3x+2}$
$\displaystyle (11)\quad \lim_{x\to0} \frac{\sqrt{1+x}-\sqrt{1-x}}{x}$	$\displaystyle (12)\quad \lim_{x\to\infty} \frac{x}{\sqrt{1+x}-\sqrt{1-x}}$	$\displaystyle (13)\quad \lim_{x\to0} \frac{\sin 2x+x\cos x+\tan 4x}{x+\sin 3x}$
$\displaystyle (14)\quad \lim_{x\to+0} \frac{\log(1+x)}{x}$	$\displaystyle (15)\quad \lim_{x\to0} \frac{e^x-1}{x}$	$\displaystyle (16)\quad \lim_{x\to+0} \frac{2}{1+e^{-1/x}}$
$\displaystyle (17)\quad \lim_{x\to\infty} \frac{2x-1+e^{x}}{x^3-5x+1}$	$\displaystyle (18)\quad \lim_{x\to\infty} \frac{x^3-5x+1}{2x-1+\log x}$	$\displaystyle (19)\quad \lim_{x\to\infty} \frac{2x-1+e^{x}}{2x-1+\log x}$