Question

1. For each of the following functions: f(t) = egin{cases} 0 & t < 0 \ t^2 & 0 le t < 1 \ 2t & 1 le t end{cases} g(t) = egin{cases} 0 & t < 0 \ 4e^{-2t} & 0 le t < 2 \ t^2 & 2 le t < 3 \ 1 & 3 le t end{cases} (a) plot it. (b) write it in terms of the unit step function. (c) find its Laplace transform.

          1. For each of the following functions:

f(t) = 
egin{cases} 
0 & t < 0 \ 
t^2 & 0 le t < 1 \ 
2t & 1 le t 
end{cases} 
g(t) = 
egin{cases} 
0 & t < 0 \ 
4e^{-2t} & 0 le t < 2 \ 
t^2 & 2 le t < 3 \ 
1 & 3 le t 
end{cases}

(a) plot it.
(b) write it in terms of the unit step function.
(c) find its Laplace transform.

1. For each of the following functions:

f(t) =
egincases
0 t < 0
t^2 0 le t < 1
2t 1 le t
endcases
g(t) =
egincases
0 t < 0
4e^-2t 0 le t < 2
t^2 2 le t < 3
1 3 le t
endcases

(a) plot it.
(b) write it in terms of the unit step function.
(c) find its Laplace transform.

Added by Katherine N.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/06/2023

Step 1

Write the functions in terms of the unit step function: For f(t): f(t) = 4e^{-2t}u(t) - 4e^{-2t}u(t-2) + 2u(t-2) - 2u(t-3) For g(t): g(t) = t^2u(t) - (t^2 - 2t + 1)u(t-1) Show more…

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