| \(\lim_{x \to 0^-} \frac{1}{x} = - \infty\) | | \(\lim_{x \to 0^+} \frac{1}{x} = + \infty\) | |
| \(\lim_{x \to -\infty} \frac{1}{x} = 0\) | | \(\lim_{x \to +\infty} \frac{1}{x} = 0\) | |
| \(\lim_{x \to -\infty} \frac{1}{x^n} = 0\) | | \(\lim_{x \to 0} \frac{1}{x} \) neexistuje | |
| Je-li \(a \in (0,\,1)\) |
| \(\lim_{x \to -\infty} a^x = + \infty\) | | \(\lim_{x \to +\infty} a^x = 0\) | |
| \(\lim_{x \to 0^+} \mathrm{log}_a x = + \infty\) | | \(\lim_{x \to +\infty} \mathrm{log}_a x = - \infty\) | |
| Je-li \(a \in (1,\,+ \infty)\) |
| \(\lim_{x \to -\infty} a^x = 0\) | | \(\lim_{x \to +\infty} a^x = +\infty\) | |
| \(\lim_{x \to 0^+} \mathrm{log}_a x = - \infty\) | | \(\lim_{x \to +\infty} \mathrm{log}_a x = + \infty\) | |
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| \(\lim_{x \to 0^+} \mathrm{ln} x = - \infty\) | | \(\lim_{x \to +\infty} \mathrm{ln} x = + \infty\) | |
| \(\lim_{x \to -\infty} \sin x \) neexistuje | | \(\lim_{x \to +\infty} \sin x \) neexistuje | |
| \(\lim_{x \to -\infty} \cos x \) neexistuje | | \(\lim_{x \to +\infty} \cos x \) neexistuje | |
| \(\lim_{x \to \frac{\pi}{2}^-} \mathrm{tg} x = + \infty\) | | \(\lim_{x \to \frac{\pi}{2}^+} \mathrm{tg} x = - \infty\) | |
| \(\lim_{x \to 0^-} \mathrm{cotg} x = - \infty\) | | \(\lim_{x \to 0^+} \mathrm{cotg} x = + \infty\) | |
| \(\lim_{x \to 0} \frac{\sin x}{x} = 1\) | | \(\lim_{x \to 0} \frac{\mathrm{tg} x}{x} = 1\) | |
| \(\lim_{x \to 0} \frac{e^x - 1}{x} = 1\) | | \(\lim_{x \to 0} \frac{\mathrm{ln} (1 + x)}{x} = 1\) | |
