Find the following limits $($if exist$)$

i$)\underset{x-2}{lim}f(x)$

ii$)\underset{x-1}{lim}f(x)$

iii$)\underset{x0}{lim}f(x)$

iv$)\underset{x\frac{1}{2}}{lim}f(x)$

v$)\underset{x1}{lim}f(x)$

$2.$

Consider the following statements

i$)\underset{x{0}^{-}}{lim}f(x)=0$

iv$)\underset{x{1}^{-}}{lim}f(x)=-1$

ii$)\underset{x{0}^{}}{lim}f(x)=0$

v$)\underset{x{1}^{}}{lim}f(x)=0$

iii$)\underset{x0}{lim}f(x)$ exists

vi$)\underset{x1}{lim}f(x)$ exists

Suppose $\underset{x4}{lim}f(x)=2$ and $\underset{x4}{lim}g(x)=-2.$ Find the following limit by using the algebra of limit

i$)\underset{x4}{lim}[f(x)4g(x)]$

ii$)\underset{x4}{lim}[2f(x)-3g(x)]$

iii$)\underset{x4}{lim}[5f(x)g(x)]$

iv$)\underset{x4}{lim}[\frac{3f(x)}{4g(x)}]$

v$)\underset{x4}{lim}[\sqrt[\phantom{2}]{f(x)}(g(x){)}^2]$