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)}


=4s415s3+10s26s414s3+5s2+12s228s10=\dfrac{4s⁴-15s³+10s²}{6s⁴-14s³+5s²+12s²-28s-10}


=4s415s3+10s26s414s3+17s228s10=\dfrac{4s⁴-15s³+10s²}{6s⁴-14s³+17s²-28s-10}

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