Help about limits, please!!!

How to calculate this limit:
lim(x→2^- )⁡ ((g(x)-g(2))/(x-2) where f(x)={(x, if x≥2 and (x²)/(2), if x<2)}

ps: 2^- means that the limit is to the left.

I imagine you meant to type g(x) instead of f(x). In that case, g(2) = 2, and g(x) = (x^2)/2 for x<2. You can then just simplify:

(g(x)-g(2))/(x-2)
= ((x^2)/2 - 2) / (x-2)
= ((x/2) - 1)(x + 2)) / (x-2)
= 1/2 * (x-2)(x+2) / (x-2)
= 1/2 * (x+2)

The limit of this as x goes to 2 from the left is just 2.