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181.
$\lim{x \to \infty} \left(1+\dfrac{1}{x}\right)^x=e$
E
Limit
182.
$\lim{x\to\infty}\left(1-\dfrac{1}{x}\right)^x=\dfrac{1}{e}$
Limit
E
183.
$\lim{x \to 0}\left(1+x\right)^\frac{1}{x} = e$
E
Limit
184.
$\lim{x \to 0}\left(1+kx\right)^\frac{m}{x}=e^{km}$
E
Limit
185.
$\lim {x \to \infty}\left(\dfrac{x}{x+k}\right)^x=e^{-k}$
E
Limit
186.
$\lim{x \to \infty} \dfrac{x}{e^x} = 0$
E
Limit
187.
$\lim{x \to 0} \left(\dfrac{e^x-1}{x}\right) = 1$
E
Limit
188.
$\lim{x \to 0} \left(\dfrac{a^x-1}{x}\right)=\ln a$
Limit
Logarithm
189.
$\lim {x \to 0} \left(\dfrac{e^{ax}-1}{x}\right)=a$
E
Limit
190.
$\lim{x \to 1} \left( \dfrac{\ln x}{x-1} \right)=1$
Limit
Logarithm
191.
$\lim{x \to 0} \dfrac{\ln(x+1)}{x}=1$
Limit
Logarithm
192.
$\lim{x \to 0^+}x\ln x = 0$
Limit
Logarithm
193.
$\lim{x \to \infty}\dfrac{\ln x}{x} =0$
Limit
Logarithm
194.
$\lim{n \to \infty} \left( \sum^n_{k=1} \dfrac{1}{k} - \ln n \right) = ℽ$
Limit
195.
$\lim{n \to \infty} \dfrac{n}{\sqrt[n]{n!}}=e$
Limit
196.
$\lim{n \to \infty} \left(n!\right)^{1/n}=\infty$
Limit
197.
$\dfrac{d}{dx}\, \left(C\right) = 0$
Differentiation
198.
$\dfrac{d}{dx}\, \left(x\right) = 1$
Differentiation
199.
$\dfrac{d}{dx}\, \left(ax+b\right) = a$
Differentiation
200.
$\dfrac{d}{dx}\, \left(x^{-n}\right) = -\dfrac{n}{x^{n+1}}$
Differentiation

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