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Ta có cos\sqrt{x} \sim 1 -\frac{x}{2} ( x \rightarrow 0). Do đó \mathop {\lim }\limits_{x \to 0} \sqrt[x]{cos\sqrt{x}}=\mathop {\lim }\limits_{x \to 0}(1-\frac{x}{2})^{\frac{1}{x}} =\mathop {\lim }\limits_{x \to 0}(1-\frac{x}{2})^{\frac{-2}{x}.\frac{1}{-2}} =\frac{1}{\sqrt{e}}.
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