Answer to Question #223813 in Chemical Engineering for Lokika

Question

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

Answer 1

$F(s) = \dfrac{s²+2}{s(2s²-7s+5)}$

$= \dfrac{s²+3}{2s³-7s²+5s}$

Using quotient rule

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

$F(s) =\dfrac{Vdu-Udv}{V²}$

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

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

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