Kết quả \(\underset{x\to -1}{\mathop{\lim }}\,\frac{x+1}{2{{x}^{3}}+2}\) bằng:

* Hướng dẫn giải

Ta có:

\(\underset{x\to -1}{\mathop{\lim }}\,\frac{x+1}{2{{x}^{3}}+2}=\underset{x\to -1}{\mathop{\lim }}\,\frac{x+1}{2\left( {{x}^{3}}+1 \right)}=\underset{x\to -1}{\mathop{\lim }}\,\frac{x+1}{2\left( x+1 \right)\left( {{x}^{2}}-x+1 \right)}=\underset{x\to -1}{\mathop{\lim }}\,\frac{1}{2\left( {{x}^{2}}-x+1 \right)}=\frac{1}{2.3}=\frac{1}{6}.\)