- Thread starter
- Moderator
- #1
- Jan 26, 2012
- 995
Thanks again to those who participated in last week's POTW! Here's this week's problem!
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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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Remember to read the POTW submission guidelines to find out how to submit your answers!
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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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Remember to read the POTW submission guidelines to find out how to submit your answers!