tính [tex]\lim_{x\to 1}\frac{\sqrt{x^{2}+x+2}-\sqrt[3]{7x+1}}{\sqrt{2}(x-1)}[/tex]
[tex]\lim_{x\to 1}\frac{\sqrt{x^{2}+x+2}-\sqrt[3]{7x+1}}{\sqrt{2}(x-1)}[/tex]
[tex]=\lim_{x\to 1}\frac{(\sqrt{x^{2}+x+2}-(x+1))-(\sqrt[3]{7x+1}-(x+1))}{\sqrt{2}(x-1)}[/tex]
[tex]=\lim_{x\to 1}\frac{\sqrt{x^{2}+x+2}-(x+1)}{\sqrt{2}(x-1)}-\frac{\sqrt[3]{7x+1}-(x+1)}{\sqrt{2}(x-1)}[/tex]
[tex]=\lim_{x\to 1}\frac{x^{2}+x+2-(x+1)^{2}}{\sqrt{2}(x-1)(\sqrt{x^{2}+x+2}+(x+1))}-\frac{7x+1-(x+1)^{3}}{\sqrt{2}(x-1)(\sqrt[3]{7x+1}^{2}+\sqrt[3]{7x+1}(x+1)+(x+1)^{2})}[/tex](dùng nhân liên hợp)
[tex]=\lim_{x\to 1}\frac{-x+1}{\sqrt{2}(x-1)(\sqrt{x^{2}+x+2}+(x+1))}-\frac{-x^{3}-3x^{2}+4x}{\sqrt{2}(x-1)(\sqrt[3]{7x+1}^{2}+\sqrt[3]{7x+1}(x+1)+(x+1)^{2})}[/tex]
[tex]=\lim_{x\to 1}\frac{-1}{\sqrt{2}(\sqrt{x^{2}+x+2}+(x+1))}-\frac{-x(x+4)}{\sqrt{2}(\sqrt[3]{7x+1}^{2}+\sqrt[3]{7x+1}(x+1)+(x+1)^{2})}=\frac{\sqrt{2}}{12}[/tex]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
