tính [tex]\lim_{x\to1} \frac{\sqrt{x^{2}+x+2}-\sqrt[3]{2x^{3}+5x+1}}{x^{2}-1}[/tex]
[tex]\lim_{x\to1} \frac{\sqrt{x^{2}+x+2}-\sqrt[3]{2x^{3}+5x+1}}{x^{2}-1}[/tex]
[tex]=\lim_{x\to1} \frac{\sqrt{x^{2}+x+2}-(x+1)-(\sqrt[3]{2x^{3}+5x+1}-(x+1))}{x^{2}-1}[/tex]
[tex]=\lim_{x\to1} \frac{\sqrt{x^{2}+x+2}-(x+1)}{x^{2}-1}-\frac{\sqrt[3]{2x^{3}+5x+1}-(x+1)}{x^{2}-1}[/tex]
[tex]=\lim_{x\to1} \frac{x^{2}+x+2-(x+1)^{2}}{(x^{2}-1)(\sqrt{x^{2}+x+2}+(x+1))}-\frac{2x^{3}+5x+1-(x+1)^{3}}{(x^{2}-1)(\sqrt[3]{2x^{3}+5x+1}^{2}+\sqrt[3]{2x^{3}+5x+1}(x+1)+(x+1)^{2})}[/tex]
[tex]=\lim_{x\to1} \frac{-x+1}{(x^{2}-1)(\sqrt{x^{2}+x+2}+(x+1))}-\frac{x(x^{2}-3x+2)}{(x^{2}-1)(\sqrt[3]{2x^{3}+5x+1}^{2}+\sqrt[3]{2x^{3}+5x+1}(x+1)+(x+1)^{2})}[/tex]
[tex]=\lim_{x\to1} \frac{-1}{(x+1)(\sqrt{x^{2}+x+2}+(x+1))}-\frac{x(x-2)}{(x+1)(\sqrt[3]{2x^{3}+5x+1}^{2}+\sqrt[3]{2x^{3}+5x+1}(x+1)+(x+1)^{2})}[/tex]
[tex]=-\frac{1}{12}[/tex]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
