a) Find b) Find c) Find d) Check the results of parts (a), (b), and (c) by first
Chapter 12, Problem 12.22(choose chapter or problem)
a) Find \(\mathscr{L}\left\{\frac{d}{d t} \sin \omega t\right\}\).
b) Find \(\mathscr{L}\left\{\frac{d}{d t} \cos \omega t\right\}\).
c) Find \(\mathscr{L}\left\{\frac{d^{3}}{d t^{3}} t^{2} u(t)\right\}\).
d) Check the results of parts (a), (b), and (c) by first differentiating and then transforming.
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