Tổng hợp đầy đủ những giới hạn hay gặp mà học sinh không thể bỏ qua

$\displaystyle \lim_{x\to\infty}e^x= \infty$

$\displaystyle \lim_{x\to-\infty}e^x= 0$

$\displaystyle \lim_{x\to0}a^x= 1$

$\displaystyle \lim_{x\to\infty}lnx= \infty$

$\displaystyle \lim_{x\to\infty}\dfrac{c}{x^n}= 0 (n>0)$

$\displaystyle \lim_{x\to\infty}\dfrac{x}{^x \sqrt{x!}}= e$

$\displaystyle \lim_{x\to\infty}(1+ \dfrac{k}{x})^x= e^k, e =2.71$

$\displaystyle \lim_{x\to\infty}(1- \dfrac{1}{x})^x= \dfrac{1}{e}$

$\displaystyle \lim_{x\to\infty}\dfrac{x!}{x^xe^{-x}\sqrt{x}}= \sqrt{2 \pi}$

$\displaystyle \lim_{x\to\infty}log_a(1+\dfrac{1}{x})^x=log _a e$

$\displaystyle \lim_{x\to0} \dfrac{log_e(1+x)}{x}=1$

$\displaystyle \lim_{x\to0}\dfrac{x}{log_a(1+x)}= \dfrac{1}{log_ae}$

$\displaystyle \lim_{x\to0}\dfrac{a^x-1}{x}= ln \ a, a>0$

$\displaystyle \lim_{x\to0}\dfrac{sinx}{x}= 1$

$\displaystyle \lim_{x\to0}\dfrac{tanx}{x}= 1$

$\displaystyle \lim_{x\to0}\dfrac{1-cosx}{x}= 0$

$\displaystyle \lim_{x\to0}\dfrac{1-cosx}{x^2}= \dfrac{1}{2}$

$\displaystyle \lim_{x\to0}\dfrac{arcsinx}{x}= 1$

$\displaystyle \lim_{x\to0}\dfrac{arctanx}{x}= 1$

$\displaystyle \lim_{x\to0}\dfrac{(arccosx)^2}{1-x}= 2$