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Ta có:
\mathop {\lim }\limits_{x \to 1}\dfrac{\sqrt{5-x^3}-\sqrt[3]{x^2+7}}{x^2-1}
=\mathop {\lim }\limits_{x \to 1}\dfrac{(\sqrt{5-x^3}-2)+(2-\sqrt[3]{x^2+7})}{x^2-1}
=\mathop {\lim }\limits_{x \to 1}\dfrac{\dfrac{1-x^3}{\sqrt{5-x^3}+2}-\dfrac{1-x^2}{4+2\sqrt[3]{x^2+7}+\sqrt[3]{(x^2+7)^2}}}{x^2-1}
=\mathop {\lim }\limits_{x \to
1}\dfrac{-\dfrac{1+x+x^2}{\sqrt{5-x^3}+2}+\dfrac{1+x}{4+2\sqrt[3]{x^2+7}+\sqrt[3]{(x^2+7)^2}}}{x+1}=\dfrac{-7}{24}
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