��ʬ��ʬ�س���AI���� No.9

���� 9.1 (�Ʒ�)   [``���ʽ����� 10''] �˸� $\lim_{x\to x_0} f(x)$ �� $\lim_{x\to x_0} g(x)$ ���Ȥ�� ¸�ߤ���Ȳ��ꤹ�롣���ΤȤ������Τ��Ȥ�����Ω�ġ�

1. $$\lim_{x\to x_0} (f(x) \pm g(x)) =\lim_{x\to x_0} f(x) \pm \lim_{x\to x_0} g(x).$$
2. $$\lim_{x\to x_0} c f(x)= c \lim_{x\to x_0} f(x)$$ .
3. $$\lim_{x\to x_0} (f(x) g(x)) =\left(\lim_{x \to x_0} f(x)\right) \left( \lim_{x\to x_0} g(x) \right).$$
4. ����ˡ� $\lim_{x\to x_0} f(x) \neq 0$ �Ȳ��ꤹ��ȡ�
   $$\lim_{x\to x_0} (g(x)/ f(x)) =\left(\lim_{x\to x_0} g(x)\right)/ \left( \lim_{x\to x_0} f(x) \right).$$

����μ�«�ȴؿ��μ�«�ˤϼ��Τ褦�ʴط������롣

���� 9.2   $x_0$ �ζ᤯��������줿�ؿ� $f$ �ˤ������ơ� ���Τ��Ȥ�Ʊ�ͤǤ��롣

1. $f$ �� $x\to x_0$ �Ǥζ˸¤�¸�ߤ��롣
2. $a_n \to x_0$ �ǡ� $a_n \neq x_0 (\forall n)$ �ʤ�Ǥ�դο��� $\{ a_n\}_{n=1}^\infty$ �ˤ������ơ� $\{f(a_n)\}_{n=1}^\infty$ �Ϥ����ͤ˼�«���롣

���� 9.1   ���ο� $\epsilon>0$ ��Ϳ�����Ƥ���Ȥ��롣 ���ΤȤ��� ���Τ褦�� ���ο� $\delta$ �ò¸«¤Ä¤ï¿½ï¿½Ê¤ï¿½ï¿½ï¿½ï¿½ï¿½

$$\forall b \left( \vert b-5\vert<\delt... ...text{ and } \left\vert\frac{1}{b}-\frac{1}{5} \right\vert <\epsilon ) \right)$$