Answer to Question #223813 in Chemical Engineering for Lokika

Question #223813

If F(s)=s^{2}+2/s(2s^{2}-7s+5); then lim t→∞f(t)


1
Expert's answer
2021-08-09T08:04:25-0400

F(s)=s²+2s(2s²7s+5)F(s) = \dfrac{s²+2}{s(2s²-7s+5)}


=s²+32s³7s²+5s= \dfrac{s²+3}{2s³-7s²+5s}


Using quotient rule

u=s²+2;  du=2sv=2s³7s²+5s;  dv=6s²14s+5u = s²+2;\ \ du = 2s\\ v = 2s³-7s²+5s; \ \ dv= 6s²-14s+5


F(s)=VduUdvV²F(s) =\dfrac{Vdu-Udv}{V²}


F(s)=2s(2s³7s²+5s)(s²+2)(6s²14s+5)F'(s) = \dfrac{2s(2s³-7s²+5s)}{(s²+2)(6s²-14s+5)}


=4s15s³+10s²6s14s³+5s²+12s²28s10=\dfrac{4s⁴-15s³+10s²}{6s⁴-14s³+5s²+12s²-28s-10}


=4s15s³+10s²6s14s³+17s²28s10=\dfrac{4s⁴-15s³+10s²}{6s⁴-14s³+17s²-28s-10}

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