Cho hàm số $y=f(x)=\frac{1-4x^2}{(2x-1)(x+3)}$.
1. Tính $\underset{x\to \frac{1}{2}}{\lim }f(x)$.
2. Tính $\underset{x\to (-3{)}^{+}}{\lim }f(x)$.
3. Tính $\underset{x\to (-3{)}^{-}}{\lim }f(x)$.
4. Tính $\underset{x\to +\infty }{\lim }f(x)$; $\underset{x\to -\infty }{\lim }f(x)$.
5. Tính $\underset{x\to +\infty }{\lim }\left[x.f(x)\right]$.
6. $\underset{x\to -\infty }{\lim }\left(\frac{f(x)}{x}\right)$.