Question

Find the Laplace transform of (f(t) = e^{4t} + 5). frac{6s+20}{s^2-4s} frac{6s-20}{s^2-4s} frac{6s-20}{s^3-4s} frac{6s-20}{s^2+4s} Find the Laplace transform of (f(t) = e^{-2t} cos (3t) + 5e^{-2t} sin (3t)). frac{s+17}{(s+2)^2+9} frac{s+17}{(s+2)^2-9} frac{s+17}{(s+2)^2-9} frac{s+17}{(s-2)^2+9} Find the Laplace of (f(t) = 4 sin(3t) + 2 cos(9t)). frac{2s^3+12s^2+18s+972}{(s^2-9)(s^2+81)} frac{2s^3+12s^2+18s+972}{(s^2+9)(s^2+81)} frac{2s^3+12s^2+18s+972}{(s^2+9)(s^2-81)} frac{2s^3-12s^2+18s-972}{(s^2+9)(s^2+81)} Find the (L{(t^2 + 4t + 2)e^{3t}}). frac{2s^3-8s+8}{(s+3)^3} frac{2s^3-8s+8}{(s-3)^3} frac{2s^3-8s-8}{(s-3)^3} frac{2s^3+8s+8}{(s-3)^3}

          Find the Laplace transform of (f(t) = e^{4t} + 5).
frac{6s+20}{s^2-4s}
frac{6s-20}{s^2-4s}
frac{6s-20}{s^3-4s}
frac{6s-20}{s^2+4s}
Find the Laplace transform of (f(t) = e^{-2t} cos (3t) + 5e^{-2t} sin (3t)).
frac{s+17}{(s+2)^2+9}
frac{s+17}{(s+2)^2-9}
frac{s+17}{(s+2)^2-9}
frac{s+17}{(s-2)^2+9}
Find the Laplace of (f(t) = 4 sin(3t) + 2 cos(9t)).
frac{2s^3+12s^2+18s+972}{(s^2-9)(s^2+81)}
frac{2s^3+12s^2+18s+972}{(s^2+9)(s^2+81)}
frac{2s^3+12s^2+18s+972}{(s^2+9)(s^2-81)}
frac{2s^3-12s^2+18s-972}{(s^2+9)(s^2+81)}
Find the (L{(t^2 + 4t + 2)e^{3t}}).
frac{2s^3-8s+8}{(s+3)^3}
frac{2s^3-8s+8}{(s-3)^3}
frac{2s^3-8s-8}{(s-3)^3}
frac{2s^3+8s+8}{(s-3)^3}

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$Find the Laplace transform of (f(t) = e^4t + 5). frac6s+20s^2-4s frac6s-20s^2-4s frac6s-20s^3-4s frac6s-20s^2+4s Find the Laplace transform of (f(t) = e^-2t cos (3t) + 5e^-2t sin (3t)). fracs+17(s+2)^2+9 fracs+17(s+2)^2-9 fracs+17(s+2)^2-9 fracs+17(s-2)^2+9 Find the Laplace of (f(t) = 4 sin(3t) + 2 cos(9t)). frac2s^3+12s^2+18s+972(s^2-9)(s^2+81) frac2s^3+12s^2+18s+972(s^2+9)(s^2+81) frac2s^3+12s^2+18s+972(s^2+9)(s^2-81) frac2s^3-12s^2+18s-972(s^2+9)(s^2+81) Find the (L(t^2 + 4t + 2)e^3t). frac2s^3-8s+8(s+3)^3 frac2s^3-8s+8(s-3)^3 frac2s^3-8s-8(s-3)^3 frac2s^3+8s+8(s-3)^3$

Added by Mario S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Rosina Dapaah

12/18/2021

Step 1

Step 1: To find the Laplace transform of \( f(t) = e^{4t} + 5 \), we use the linearity of the Laplace transform and the fact that the Laplace transform of \( e^{at} \) is \( \frac{1}{s-a} \) and the Laplace transform of a constant is \( \frac{constant}{s} \) where Show more…

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Find the Laplace transform of f(t) = e^4t + 5. Find the Laplace of f(t) = 4sin(3t) + 2 cos(9t) Find the Laplace transform of f(t) = e^-2t cos(3t) + 5e^-2t sin(3t). Find the L{(t^2 + 4t + 2)e^3t}.

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Transcript

00:01 So in our question, we've been given that f of t is equal to e to the power 4 t plus 5.

00:13 So this implies that if you are supposed to find f of l of f of t, this will be l of a to the power of 40 plus 5.

00:28 So simplifying this, you're going to get l of e to the power 40 plus l of 5.

00:36 So from here we are going to get 1 over s minus 4 plus 5 times 1 over s.

00:48 So based on this answer, it implies that if you are given l of a to the power a t, you are going to get 1 over s minus a.

01:02 And if you are given l of 1, you will be equal to 1 times 1 over s.

01:10 Which is the same as 1 over s.

01:15 So continue with our simplification, you're going to get s plus 5 into bracket s minus 4.

01:23 Divided by s times s minus 4.

01:30 So we get s minus 20 over s squared minus 4 s.

01:39 So now the second option is true.

01:43 So going to the next one, saying it's giving that f of t is equal to 4 sign 3 t plus 90.

02:06 So applying the same rule, getting l of f of t will be equal to l of sine 3t plus 90.

02:26 So simplifying this, you're going to bring four outside.

02:32 Then you're going to get l over here.

02:50 So we get sign 3t plus 2 outside.

03:01 We have l plus 90.

03:11 So this implies that i'm going to get four times.

03:16 You have 3 divided by s squared plus 3 squared plus 2 times s over.

03:28 You have s squared plus nine squared so this is based on when you are given l of sign b t you will be equal to b over s squared plus b squared and when you are given l of course b t this is equal to s over s squared plus b b this is equal to so now continue with our simplification.

04:14 We are going to get 12 over s squared plus 9 plus 2s over s squared plus 81...

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