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- Jan 26, 2012

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**Problem**: Let

\[f(t)=\begin{cases}\dfrac{\sin t}{t}, & t\neq 0\\ 1, & t=0.\end{cases}\]

(a) Find the Taylor series for $f$ about $0$.

(b) Assuming that the Laplace transform can be computed term by term, verify that $\mathcal{L}\{f(t)\}=\arctan(1/s)$ for $s>1$.

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