g(x) = {-x, x<=0

3x^2,x>0

(a) Evaluate the limit of {g(x+delta x) - g(x)}/{delta x) for x<=0 and x>0 as delta x tends to 0

(b) evaluate the limit of {g(delta x) - g(0)}/{delta x) as delta x tends to 0 from the right and as delta x tends to 0 from the left

(c) sketch the graph of g'(x)

Is g(x) continuous at x=0?

I need help with (b) and (c) only. Is there any user-friendly programmes to type the equations? I find the syntax of latex very difficult to learn. Btw, how do you type the above equations (using latex)?

Thanks!