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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