Evaluate the following limits:

$($a$)\underset{x0}{lim}\frac{sin(x)}{x}$

$($b$)\underset{x}{lim}\frac{2x^{2}3x}{x^2-5}$

$($c$)\underset{x1}{lim}\frac{x^2-1}{x-1}$

Find the value of $k$ that makes the function continuous on $R$ :

$f(x)=\{\begin{array}{cc}{x}^2& kfx<mn>2</mn>\\ 4x-3\text{i}\text{f}\text{x}& 2\end{array}$