Question

One property of Laplace transforms can be expressed in terms of the inverse Laplace transform as 2-1 d'F }(t)= (-t)"f(t), where f= 2-{F}. Use this equation to compute 2-1{F} ds 25 F(s) = arctan S Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms.

Answer 1

j Solution; given F(S) = tant(s); Then 1-"{F(s} = ? If l{+()} = FLS) ; L'{FUJS = fuas Then L&+ f(+5) = -(FCS] +16) H{ d(fal} f(A) Fos) = - Af (0) ${"{ (ps]} booty ds use This formula to evaluating tant d fles TT = f(0) S2 of (25) → 1/2 L { a los tant (39]} 5941409 17 - and to 4* { content » [since { az} = sin at 82 S24 (25)2 S2 } = flos } f14) (1) =

Now using above Prapertues we can brite eah cij eie [sin 251] = f(0) t sin ast t Ans Hence f(+) = 4{FLSJS = Please like me for good CF Score and if any Problem in This solution Then Comment me.