1.
limx0sinxx=1\lim_{x\to 0} \dfrac{\sin x}{x}=1
2.
limx0sinaxbx=ab\lim_{x\to 0} \dfrac{\sin ax}{bx}=\dfrac{a}{b}
3.
limxxsin(1x)=1\lim_{x\to\infty} x \sin \left( \dfrac{1}{x} \right) = 1
4.
limx01cosxx=0\lim_{x \to 0} \dfrac{1-\cos x}{x}=0
5.
limx01cosxx2=12\lim_{x \to 0} \dfrac{1-\cos x}{x^2}=\dfrac{1}{2}
6.
limx0tanxx=1\lim{x \to 0} \dfrac{\tan x}{x}=1
7.
limx0tanaxbx=ab\lim{x \to 0} \dfrac{\tan ax}{bx}=\dfrac{a}{b}
8.
limx(1+1x)x=e\lim{x \to \infty} \left(1+\dfrac{1}{x}\right)^x=e
9.
limx(11x)x=1e\lim{x\to\infty}\left(1-\dfrac{1}{x}\right)^x=\dfrac{1}{e}
10.
limx(1+kx)mx=ekm\lim{x \to \infty}\left(1+\dfrac{k}{x}\right)^{mx}=e^{km}
11.
limx0(1+x)1x=e\lim{x \to 0}\left(1+x\right)^\frac{1}{x} = e
12.
limx0(1+kx)mx=ekm\lim{x \to 0}\left(1+kx\right)^\frac{m}{x}=e^{km}
13.
limx(xx+k)x=ek\lim {x \to \infty}\left(\dfrac{x}{x+k}\right)^x=e^{-k}
14.
limxxex=0\lim{x \to \infty} \dfrac{x}{e^x} = 0
15.
limx0(ex1x)=1\lim{x \to 0} \left(\dfrac{e^x-1}{x}\right) = 1
16.
limx0(ax1x)=lna\lim{x \to 0} \left(\dfrac{a^x-1}{x}\right)=\ln a
17.
limx0(eax1x)=a\lim {x \to 0} \left(\dfrac{e^{ax}-1}{x}\right)=a
18.
limx1(lnxx1)=1\lim{x \to 1} \left( \dfrac{\ln x}{x-1} \right)=1
19.
limx0ln(x+1)x=1\lim{x \to 0} \dfrac{\ln(x+1)}{x}=1
20.
limx0+xlnx=0\lim{x \to 0^+}x\ln x = 0
21.
limxlnxx=0\lim{x \to \infty}\dfrac{\ln x}{x} =0
22.
limn(k=1n1klnn)=\lim{n \to \infty} \left( \sum^n_{k=1} \dfrac{1}{k} - \ln n \right) = ℽ
23.
limnnn!n=e\lim{n \to \infty} \dfrac{n}{\sqrt[n]{n!}}=e
24.
limn(n!)1/n=\lim{n \to \infty} \left(n!\right)^{1/n}=\infty