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limit:limit [2014/01/13 21:02] marje created |
limit:limit [2014/12/12 21:21] jaan Fixed error: these formulas only hold for a > 1 |
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| Some well-known limits: | Some well-known limits: | ||
| - | * $\lim_{x \to \infty} \frac{x^d}{a^{x}} = 0$ for any constants $a > 0, d > 0$. | + | * $\lim_{x \to \infty} \frac{x^d}{a^{x}} = 0$ for any constants $a > 1, d > 0$. |
| - | * $\lim_{x \to \infty} \frac{x^d}{(\log_a x)^b} = \infty$ for any constants $a > 0, b > 0, d > 0$. | + | * $\lim_{x \to \infty} \frac{x^d}{(\log_a x)^b} = \infty$ for any constants $a > 1, b > 0, d > 0$. |
| ===== Exercises ===== | ===== Exercises ===== | ||