<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">Spočtěte následující limity:
$$
\lim_{x \to y}\frac{x^n - y^n}{x - y} \quad n \in \Bbb N, \\
\lim_{x \to +\infty}\frac{\sqrt{x+2} - \sqrt{x+1}}{\sqrt{x+3} -
\sqrt{x+1}}, \qquad \\
\lim_{x \to 0}\frac{\sin{x^2}}{x^2}.
$$
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