(Answer Ally IWU Find the Laplace t...
Question

# (Answer Ally IWU Find the Laplace transform of (a) - {Sin VE} (b) _{sin?at}

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( (sin sqrt{2}) ) ( sin t=t-frac{t^{3}}{sqrt{3}}+frac{t^{5}}{5 !}-frac{t^{7}}{7 !}+ ) ( therefore sin sqrt{t}=t frac{1 / 2 t^{3 / 2}}{d !}+frac{t^{5 / 2}}{sigma !}-frac{t^{7 / 12}}{7 !}+cdots ) ( left{Lleft(t^{n}right)=frac{sqrt{n+1}}{k^{n}+1}right} ) ( =frac{sqrt{33 / 2}}{k^{3 / 2}}-frac{1}{3 !} frac{sqrt{5 / 2}}{b^{5 / 2}}+frac{1}{5 !} frac{sqrt{7 / 2}}{5^{7 / 2}}-frac{1}{7 !} frac{sqrt{9 / 2}}{x^{9 / 2}}+cdots ) ( =frac{frac{1}{3} sqrt{pi}}{p^{3 / 2}}-frac{1}{text { o! } frac{frac{3}{2}} cdot frac{1}{5} sqrt{x}}{b^{5 / 2}}+frac{1}{5 !} frac{5 / 2 cdot 3 / 2 cdot 1 / 2 sqrt{x}}{b^{7 / 2}}+cdots ) ( =frac{frac{1}{2} sqrt{x}}{p^{3 / 2}}left[1-frac{1}{3 !} frac{3 / 2}{p}+frac{1}{5 !} frac{frac{5}{9} cdot frac{3}{9}}{p^{2}}-cdotsright] ) ( =frac{sqrt{x}}{2 beta sqrt{b}}left[1-frac{1}{4 p}+frac{1}{2} cdot frac{1}{(4 p)^{2}}-cdotsright] ) ( =frac{sqrt{x}}{2 p sqrt{b}}left[1-frac{1}{1 ! 4 b}+frac{1}{2 !} frac{1}{(4 p)^{2}} cdot cdotsright] ) ( =frac{sqrt{x}}{2 p_{1} / p} e^{-1 / 4 p} ) ( left{because bar{e}^{x}=1-x+frac{1}{2 !} x^{2}-frac{1}{3 !} x^{3}+cdotsright} ) ( log sin sqrt{t}}=frac{sqrt{x}}{2 / sqrt{p}} e^{-1 / 4 b} )