If F(s)=s^{2}+2/s(2s^{2}-7s+5); then lim t→∞f(t)
F(s)=s²+2s(2s²−7s+5)F(s) = \dfrac{s²+2}{s(2s²-7s+5)}F(s)=s(2s²−7s+5)s²+2
=s²+32s³−7s²+5s= \dfrac{s²+3}{2s³-7s²+5s}=2s³−7s²+5ss²+3
Using quotient rule
u=s²+2; du=2sv=2s³−7s²+5s; dv=6s²−14s+5u = s²+2;\ \ du = 2s\\ v = 2s³-7s²+5s; \ \ dv= 6s²-14s+5u=s²+2; du=2sv=2s³−7s²+5s; dv=6s²−14s+5
F(s)=Vdu−UdvV²F(s) =\dfrac{Vdu-Udv}{V²}F(s)=V²Vdu−Udv
F′(s)=2s(2s³−7s²+5s)(s²+2)(6s²−14s+5)F'(s) = \dfrac{2s(2s³-7s²+5s)}{(s²+2)(6s²-14s+5)}F′(s)=(s²+2)(6s²−14s+5)2s(2s³−7s²+5s)
=4s⁴−15s³+10s²6s⁴−14s³+5s²+12s²−28s−10=\dfrac{4s⁴-15s³+10s²}{6s⁴-14s³+5s²+12s²-28s-10}=6s⁴−14s³+5s²+12s²−28s−104s⁴−15s³+10s²
=4s⁴−15s³+10s²6s⁴−14s³+17s²−28s−10=\dfrac{4s⁴-15s³+10s²}{6s⁴-14s³+17s²-28s-10}=6s⁴−14s³+17s²−28s−104s⁴−15s³+10s²
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