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