Standardgränsvärden

Standardgränsvärden
\[\lim\limits_{x \rightarrow \infty } \left( 1 + \frac{1}{x} \right)^x = \text{e}\]	\[ \lim\limits_{x \rightarrow 0 } \frac{e^x - 1 }{x} = 1\]
\[ \lim\limits_{x \rightarrow 0 } \frac{a^x - 1 }{x} = \ln(a) \]	\[ \lim\limits_{x \rightarrow \infty } e^{-x}x^a =0 \]
\[ \lim\limits_{x \rightarrow \infty } \frac{\ln(x)}{x^a} = 0, \quad (a > 0) \]	\[ \lim\limits_{x \rightarrow \infty } \frac{x^a}{b^x} = 0, \quad (b > 1)\]
\[ \lim\limits_{x \rightarrow 0 } \frac{\sin(x)}{x} = 1 \]	\[ \lim\limits_{x \rightarrow 0 } \frac{1 - cos(x)}{x^2} = \frac{1}{2}\]