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[tex]\lim_{x\to1}\frac{\sqrt{5-x^{3}}-\sqrt[3]{x^{2}+7}}{x^{2}-1}=\lim_{x\to1}\frac{\sqrt{5-x^{3}}-2x}{x^{2}-1}-\frac{\sqrt[3]{x^{2}+7}-2x}{x^{2}-1}[/tex]
[tex]=\lim_{x\to1}\frac{5-x^{3}-4x^{2}}{(x^{2}-1)(\sqrt{5-x^{3}}+2x)}-\frac{x^{2}+7-8x^{3}}{(x^{2}-1)(\sqrt[3]{x^{2}+7}^{2}+\sqrt[3]{x^{2}+7}.2x+4x^{2})}[/tex]
[tex]=\lim_{x\to1}\frac{-(x-1)(x^{2}+5x+5)}{(x-1)(x+1)(\sqrt{5-x^{3}}+2x)}-\frac{-(x-1)(8x^{2}+7x+7)}{(x-1)(x+1)(\sqrt[3]{x^{2}+7}^{2}+\sqrt[3]{x^{2}+7}.2x+4x^{2})}[/tex]
[tex]=\lim_{x\to1}\frac{-(x^{2}+5x+5)}{(x+1)(\sqrt{5-x^{3}}+2x)}-\frac{-(8x^{2}+7x+7)}{(x+1)(\sqrt[3]{x^{2}+7}^{2}+\sqrt[3]{x^{2}+7}.2x+4x^{2})}=\frac{-11}{24}[/tex]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
