Problem 예제.

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라플라스 변환

라플라스 변환

$f(t) = \dfrac{e^{at}+e^{-at}}{2}$ 의 라플라스 변환은?

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$\dfrac{s}{s^2-a^2}$

$\dfrac{a}{s^2-a^2}$

$\dfrac{s}{s^2+a^2}$

$\dfrac{a}{s^2+a^2}$

Solution

$\mathcal{L}(f(t)) = \mathcal{L} \left( \dfrac{e^{at}+e^{-at}}{2} \right) = \dfrac{1}{2} \left( \dfrac{1}{s-a}+ \dfrac{1}{s+a} \right) = \dfrac{1}{2} \left( \dfrac{s+a+s-a}{(s-a)(s+a)} \right)= \left( \dfrac{s}{s^2-a^2} \right)$

Correct answer: 1

예제.

Problem 예제.

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