1.
$\lim_{x\to 0} \dfrac{\sin x}{x}=1$
Limit
Trigonometry
2.
$\lim_{x\to 0} \dfrac{\sin ax}{bx}=\dfrac{a}{b}$
Limit
Trigonometry
3.
$\lim_{x\to\infty} x \sin \left( \dfrac{1}{x} \right) = 1$
Limit
Trigonometry
4.
$\lim_{x \to 0} \dfrac{1-\cos x}{x}=0$
Limit
Trigonometry
5.
$\lim_{x \to 0} \dfrac{1-\cos x}{x^2}=\dfrac{1}{2}$
Limit
Trigonometry
6.
$\lim{x \to 0} \dfrac{\tan x}{x}=1$
Limit
Trigonometry
7.
$\lim{x \to 0} \dfrac{\tan ax}{bx}=\dfrac{a}{b}$
Limit
Trigonometry
8.
$\lim{x \to \infty} \left(1+\dfrac{1}{x}\right)^x=e$
E
Limit
9.
$\lim{x\to\infty}\left(1-\dfrac{1}{x}\right)^x=\dfrac{1}{e}$
Limit
E
10.
$\lim{x \to \infty}\left(1+\dfrac{k}{x}\right)^{mx}=e^{km}$
E
Limit
11.
$\lim{x \to 0}\left(1+x\right)^\frac{1}{x} = e$
E
Limit
12.
$\lim{x \to 0}\left(1+kx\right)^\frac{m}{x}=e^{km}$
E
Limit
13.
$\lim {x \to \infty}\left(\dfrac{x}{x+k}\right)^x=e^{-k}$
E
Limit
14.
$\lim{x \to \infty} \dfrac{x}{e^x} = 0$
E
Limit
15.
$\lim{x \to 0} \left(\dfrac{e^x-1}{x}\right) = 1$
E
Limit
16.
$\lim{x \to 0} \left(\dfrac{a^x-1}{x}\right)=\ln a$
Limit
Logarithm
17.
$\lim {x \to 0} \left(\dfrac{e^{ax}-1}{x}\right)=a$
E
Limit
18.
$\lim{x \to 1} \left( \dfrac{\ln x}{x-1} \right)=1$
Limit
Logarithm
19.
$\lim{x \to 0} \dfrac{\ln(x+1)}{x}=1$
Limit
Logarithm
20.
$\lim{x \to 0^+}x\ln x = 0$
Limit
Logarithm
21.
$\lim{x \to \infty}\dfrac{\ln x}{x} =0$
Limit
Logarithm
22.
$\lim{n \to \infty} \left( \sum^n_{k=1} \dfrac{1}{k} - \ln n \right) = ℽ$
Limit
23.
$\lim{n \to \infty} \dfrac{n}{\sqrt[n]{n!}}=e$
Limit
24.
$\lim{n \to \infty} \left(n!\right)^{1/n}=\infty$
Limit

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