Question #223813

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

Expert's answer

"F(s) = \\dfrac{s\u00b2+2}{s(2s\u00b2-7s+5)}"

"= \\dfrac{s\u00b2+3}{2s\u00b3-7s\u00b2+5s}"

Using quotient rule

"u = s\u00b2+2;\\ \\ du = 2s\\\\\n\nv = 2s\u00b3-7s\u00b2+5s; \\ \\ dv= 6s\u00b2-14s+5"

"F(s) =\\dfrac{Vdu-Udv}{V\u00b2}"

"F'(s) = \\dfrac{2s(2s\u00b3-7s\u00b2+5s)}{(s\u00b2+2)(6s\u00b2-14s+5)}"

"=\\dfrac{4s\u2074-15s\u00b3+10s\u00b2}{6s\u2074-14s\u00b3+5s\u00b2+12s\u00b2-28s-10}"

"=\\dfrac{4s\u2074-15s\u00b3+10s\u00b2}{6s\u2074-14s\u00b3+17s\u00b2-28s-10}"

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