MTH647 Quiz 3 Set 2

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Q2. Given the piecewise function: f(t) = \begin{cases} 0, & t < 2 \\ 5, & 2 \leq t < 4 \\ 0, & t \geq 4 \end{cases} Which of the following correctly represents f(t) using unit step functions?

1. f(t)=5⋅[u(t−2)−u(t−4)]
2. f(t)=5⋅[u(t)−u(t−2)]
3. f(t)=5⋅u(t−2)
4. f(t)=5⋅[u(t−2)+u(t−4)]

Correct answer: f(t)=5⋅[u(t−2)−u(t−4)]

Q3. What is the Laplace transform of the first derivative f′(t) of a function f(t)?

1. sF(s)−f(0)
2. sF(s)+f(0)
3. (1/s)F(s)−f(0)
4. (1/s)F(s)+f(0)

Correct answer: sF(s)−f(0)

Q4. Which of the following correctly describes the relationship between the Dirac delta function δ(t) and the unit step function u(t)?

1. u(t)=δ(t)⋅ t
2. \ u(t)= {d}{dt} (t)
3. (t) = {d}{dt} u(t)
4. δ(t)=u(t)⋅t

Correct answer: (t) = {d}{dt} u(t)