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If $f: R \to R$ is defined by $f(x)= \left\{ \begin{array}{1 1} \large\frac{x-2}{x^2-3x+2} & \quad if & \quad x\in R -[1,2] \\ 2 & \quad if & \quad x=2 \\ 1 & \quad if & \quad x=2 \end{array} \right.$ then $\lim \limits_{x \to 2} \large\frac{f(x)-f(2)}{x-2}=$

$\begin {array} {1 1} (a)\;0 & \quad (b)\;-1 \\ (c)\;1 & \quad (d)\;-\frac{1}{2} \end {array}$