# Giới hạn

•   $$lim (x+y-z) = lim x+ limy - limz$$
• $$lim(xyz) = limx limy limz$$
• $$lim(\dfrac{x}{y})= \dfrac{limx}{limy}$$
• $$\lim_{x \rightarrow \alpha}[Cf(x)] = C\lim_{x \rightarrow \alpha}[f(x)]$$
• $$\lim_{x \rightarrow \alpha} [f(x)]^n = [\lim_{x \rightarrow \alpha}(f(x)]^n$$
• $$\lim_{x \rightarrow \infty} e^x= \infty$$
• $$\lim_{x \rightarrow -\infty } = 0$$
• $$\lim_{x \rightarrow 0} a^x=1$$
• $$\lim_{x \rightarrow \infty}lnx= \infty$$
• $$\lim_{x \rightarrow \infty} \dfrac{c}{x^n}= 0$$          $$(n>0)$$
• $$\lim_ {x \rightarrow \infty} \dfrac{x}{\sqrt{x!}}= e$$
• $$\lim_{x \rightarrow \infty}(1 + \dfrac{k}{x})^x= e^k, e=2.71$$
• $$\lim_{x \rightarrow \infty}(1-1\dfrac{1}{x})^x= \dfrac{1}{e}$$
• $$\lim_{x \rightarrow \infty} ( \dfrac{\sqrt{2\pi x}}{x!})^\frac{1}{x} = e$$
• $$\lim_{x \rightarrow \infty} \dfrac{x!}{x^x e^{-x}\sqrt{x}}= \sqrt{2\pi}$$
• $$\lim_{x \rightarrow \infty} log_a(1+\dfrac{1}{x})^x = log_ae$$
• $$\lim_{x \rightarrow 0} \dfrac{log_e(1+x)}{x}=1$$
• $$\lim_{x \rightarrow 0} \dfrac{x}{log_a(1+x)}= \dfrac{1}{log_ae}$$