- #1
kasse
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- 1
Homework Statement
Express f(t) = e^t, 0<t<2, using the unit step function
2. The attempt at a solution
e^t*u(t-2) is an expression for a graph of the function that is zero until t=2. My guess is
e^t*u(t+2)
Yes, the unit step function can be used to express e^t between 0 and 2. The unit step function, also known as the Heaviside function, is defined as 0 for t<0 and 1 for t≥0. By combining the unit step function with the exponential function, e^t, the result is e^t for t≥0.
The unit step function and the Heaviside function are essentially the same, with the only difference being the notation used. The unit step function is commonly denoted as u(t), while the Heaviside function is denoted as H(t).
The unit step function is defined to be 0 for t<0 and 1 for t≥0. Therefore, at t=0, the unit step function has a value of 1.
Yes, the unit step function can be used to model various real-world phenomena, such as the switching on and off of a circuit, the activation of a biochemical reaction, or the sudden change in temperature due to a heating or cooling system.
The Laplace transform of the unit step function is 1/s, where s is the Laplace variable. This can be derived by using the definition of the Laplace transform and the properties of the unit step function.