Math Doubts

Limits rules at infinity

Algebraic functions

$\displaystyle \large \lim_{x\,\to\,\pm\infty}{\normalsize \dfrac{1}{x}}$ $\,=\,$ $0$

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Exponential functions

$\displaystyle \large \lim_{x\,\to\,+\infty}{\normalsize e^x}$ $\,=\,$ $\infty$

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

$\displaystyle \large \lim_{x\,\to\,\pm\infty}{\normalsize \bigg(1+\dfrac{1}{\displaystyle x}\bigg)^x}$ $\,=\,$ $e$

Trigonometric functions

$\displaystyle \large \lim_{x\,\to\,\pm \infty}{\normalsize \dfrac{\sin{x}}{x}}$ $\,=\,$ $0$