Hàm số 

- Hướng dẫn giải

$\left.\begin{array}{l}\underset{x\to 0^{+}}{\lim }f\left(x\right)=\underset{x\to 0^{+}}{\lim }\frac{x^2}{1+x}=\frac{0^2}{1+\text{}0}=0\\ \underset{x\to 0^{-}}{\lim }f\left(x\right)=\underset{x\to 0^{+}}{\lim }\left(-x\cos x\right)=-0.c\text{os0}=0\\ f\left(0\right)=\frac{0}{1+0}=0\end{array}\right\}\Rightarrow \underset{x\to 0^{+}}{\lim }f\left(x\right)=\underset{x\to 0^{-}}{\lim }f\left(x\right)=f\left(0\right)$

$\Rightarrow$Hàm số liên tục tại x=0

$\left.\begin{array}{l}\underset{x\to 1^{+}}{\lim }f\left(x\right)=\underset{x\to 1^{+}}{\lim }{x}^3=1^3=1\\ \underset{x\to 1^{-}}{\lim }f\left(x\right)=\underset{x\to 1^{-}}{\lim }\frac{x^2}{1+x}=\frac{1^2}{1+1}=\frac{1}{2}\end{array}\right\}\Rightarrow \underset{x\to 1^{+}}{\lim }f\left(x\right)\ne \underset{x\to 1^{-}}{\lim }f\left(x\right)$