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Please answer BOTH mathematicaly on paper, and with matlab( as it says in the question). Thank youFor each of the following loop transfer function F(s), find the portion of the root locus on the real axis, asymptotes, the arrival and departure angles at any complex zero or pole, and the frequency of any imaginary-axis crossing. Sketch the root locus based on above findings. Verify your results using Matlab. Submit plots of your hand sketches and the Matlab results. a. F(s) s(s + 2)(s+5 s+8) s +1 b, F(s) =- s(s + 2)(s +5)(s +8) c. F(s)-(s+s+7) s(s+2)(s+5) (s +8)

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