Using the heaviside function write down the piecewise function that is 0 for t < 0 , t2 for t in [0,1] and t for t > 1 .

Recall that



We're looking for an equivalent form of



in terms of . For starters, we have



which takes care of the negative domain, but we have "excess function" for . To get rid of it, note that



so we can subtract this to get



Finally, we just add another shifted Heaviside function scaled by :



which can also be expressed as