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Given the functionf(x) = {{:(1-x " at " 0 le x le 1),(0 " at " 1 lt x le 2),((2-x)^(2) "at " 2 lt x le 3):} Checkdirectly that thefunctionF(x) = int_(0)^(x) f(t) dt iscontinuous on the interval [0,3] and that itsderivative at each interior point of thisinterval exists andis equalto f(x) |
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